Explanation Given: ∫ 0 5 ∫ 0 y x d x d y Calculation: ⇨ ∫ 0 5 ∫ 0 y x d x d y = ∫ π / 4 π / 2 ∫ 0 5 / sin θ r 2 cos θ d r d θ = ∫ π / 4 π / 2 cos θ d θ

CALCULUS (CLOTH)

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 16.4, Problem 11E

To determine

A sketch of the region of integration $\int_{0}^{5} \int_{0}^{y} x d x d y$ and evaluate by changing to polar coordinates.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.4, Problem 10E

Chapter 16.4, Problem 12E

Students have asked these similar questions

1) Represent I with the ordered of integration dydx 2) Represent I using polar coordinates

Q1,- A- Locate the centroid (X only) of the shaded area y=12 -3x 3 m Fig. L.A 2 m

Q4) Find plane area inside the polar function r = 2 and outside polar function r = -2cos0 in second quarter.

Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.1 - Prob. 45E Ch. 16.1 - Prob. 46E Ch. 16.1 - Prob. 47E Ch. 16.1 - Prob. 48E Ch. 16.1 - Prob. 49E Ch. 16.1 - Prob. 50E Ch. 16.1 - Prob. 51E Ch. 16.1 - Prob. 52E Ch. 16.1 - Prob. 53E Ch. 16.1 - Prob. 54E Ch. 16.1 - Prob. 55E Ch. 16.2 - Prob. 1PQ Ch. 16.2 - Prob. 2PQ Ch. 16.2 - Prob. 3PQ Ch. 16.2 - Prob. 4PQ Ch. 16.2 - Prob. 1E Ch. 16.2 - Prob. 2E Ch. 16.2 - Prob. 3E Ch. 16.2 - Prob. 4E Ch. 16.2 - Prob. 5E Ch. 16.2 - Prob. 6E Ch. 16.2 - Prob. 7E Ch. 16.2 - Prob. 8E Ch. 16.2 - Prob. 9E Ch. 16.2 - Prob. 10E Ch. 16.2 - Prob. 11E Ch. 16.2 - Prob. 12E Ch. 16.2 - Prob. 13E Ch. 16.2 - Prob. 14E Ch. 16.2 - Prob. 15E Ch. 16.2 - Prob. 16E Ch. 16.2 - Prob. 17E Ch. 16.2 - Prob. 18E Ch. 16.2 - Prob. 19E Ch. 16.2 - Prob. 20E Ch. 16.2 - Prob. 21E Ch. 16.2 - Prob. 22E Ch. 16.2 - Prob. 23E Ch. 16.2 - Prob. 24E Ch. 16.2 - Prob. 25E Ch. 16.2 - Prob. 26E Ch. 16.2 - Prob. 27E Ch. 16.2 - Prob. 28E Ch. 16.2 - Prob. 29E Ch. 16.2 - Prob. 30E Ch. 16.2 - Prob. 31E Ch. 16.2 - Prob. 32E Ch. 16.2 - Prob. 33E Ch. 16.2 - Prob. 34E Ch. 16.2 - Prob. 35E Ch. 16.2 - Prob. 36E Ch. 16.2 - Prob. 37E Ch. 16.2 - Prob. 38E Ch. 16.2 - Prob. 39E Ch. 16.2 - Prob. 40E Ch. 16.2 - Prob. 41E Ch. 16.2 - Prob. 42E Ch. 16.2 - Prob. 43E Ch. 16.2 - Prob. 44E Ch. 16.2 - Prob. 45E Ch. 16.2 - Prob. 46E Ch. 16.2 - Prob. 47E Ch. 16.2 - Prob. 48E Ch. 16.2 - Prob. 49E Ch. 16.2 - Prob. 50E Ch. 16.2 - Prob. 51E Ch. 16.2 - Prob. 52E Ch. 16.2 - Prob. 53E Ch. 16.2 - Prob. 54E Ch. 16.2 - Prob. 55E Ch. 16.2 - Prob. 56E Ch. 16.2 - Prob. 57E Ch. 16.2 - Prob. 58E Ch. 16.2 - Prob. 59E Ch. 16.2 - Prob. 60E Ch. 16.2 - Prob. 61E Ch. 16.2 - Prob. 62E Ch. 16.2 - Prob. 63E Ch. 16.2 - Prob. 64E Ch. 16.2 - Prob. 65E Ch. 16.2 - Prob. 66E Ch. 16.2 - Prob. 67E Ch. 16.2 - Prob. 68E Ch. 16.2 - Prob. 69E Ch. 16.2 - Prob. 70E Ch. 16.3 - Prob. 1PQ Ch. 16.3 - Prob. 2PQ Ch. 16.3 - Prob. 3PQ Ch. 16.3 - Prob. 1E Ch. 16.3 - Prob. 2E Ch. 16.3 - Prob. 3E Ch. 16.3 - Prob. 4E Ch. 16.3 - Prob. 5E Ch. 16.3 - Prob. 6E Ch. 16.3 - Prob. 7E Ch. 16.3 - Prob. 8E Ch. 16.3 - Prob. 9E Ch. 16.3 - Prob. 10E Ch. 16.3 - Prob. 11E Ch. 16.3 - Prob. 12E Ch. 16.3 - Prob. 13E Ch. 16.3 - Prob. 14E Ch. 16.3 - Prob. 15E Ch. 16.3 - Prob. 16E Ch. 16.3 - Prob. 17E Ch. 16.3 - Prob. 18E Ch. 16.3 - Prob. 19E Ch. 16.3 - Prob. 20E Ch. 16.3 - Prob. 21E Ch. 16.3 - Prob. 22E Ch. 16.3 - Prob. 23E Ch. 16.3 - Prob. 24E Ch. 16.3 - Prob. 25E Ch. 16.3 - Prob. 26E Ch. 16.3 - Prob. 27E Ch. 16.3 - Prob. 28E Ch. 16.3 - Prob. 29E Ch. 16.3 - Prob. 30E Ch. 16.3 - Prob. 31E Ch. 16.3 - Prob. 32E Ch. 16.3 - Prob. 33E Ch. 16.3 - Prob. 34E Ch. 16.3 - Prob. 35E Ch. 16.3 - Prob. 36E Ch. 16.3 - Prob. 37E Ch. 16.3 - Prob. 38E Ch. 16.3 - Prob. 39E Ch. 16.3 - Prob. 40E Ch. 16.3 - Prob. 41E Ch. 16.3 - Prob. 42E Ch. 16.3 - Prob. 43E Ch. 16.3 - Prob. 44E Ch. 16.3 - Prob. 45E Ch. 16.3 - Prob. 46E Ch. 16.4 - Prob. 1PQ Ch. 16.4 - Prob. 2PQ Ch. 16.4 - Prob. 3PQ Ch. 16.4 - Prob. 4PQ Ch. 16.4 - Prob. 5PQ Ch. 16.4 - Prob. 1E Ch. 16.4 - Prob. 2E Ch. 16.4 - Prob. 3E Ch. 16.4 - Prob. 4E Ch. 16.4 - Prob. 5E Ch. 16.4 - Prob. 6E Ch. 16.4 - Prob. 7E Ch. 16.4 - Prob. 8E Ch. 16.4 - Prob. 9E Ch. 16.4 - Prob. 10E Ch. 16.4 - Prob. 11E Ch. 16.4 - Prob. 12E Ch. 16.4 - Prob. 13E Ch. 16.4 - Prob. 14E Ch. 16.4 - Prob. 15E Ch. 16.4 - Prob. 16E Ch. 16.4 - Prob. 17E Ch. 16.4 - Prob. 18E Ch. 16.4 - Prob. 19E Ch. 16.4 - Prob. 20E Ch. 16.4 - Prob. 21E Ch. 16.4 - Prob. 22E Ch. 16.4 - Prob. 23E Ch. 16.4 - Prob. 24E Ch. 16.4 - Prob. 25E Ch. 16.4 - Prob. 26E Ch. 16.4 - Prob. 27E Ch. 16.4 - Prob. 28E Ch. 16.4 - Prob. 29E Ch. 16.4 - Prob. 30E Ch. 16.4 - Prob. 31E Ch. 16.4 - Prob. 32E Ch. 16.4 - Prob. 33E Ch. 16.4 - Prob. 34E Ch. 16.4 - Prob. 35E Ch. 16.4 - Prob. 36E Ch. 16.4 - Prob. 37E Ch. 16.4 - Prob. 38E Ch. 16.4 - Prob. 39E Ch. 16.4 - Prob. 40E Ch. 16.4 - Prob. 41E Ch. 16.4 - Prob. 42E Ch. 16.4 - Prob. 43E Ch. 16.4 - Prob. 44E Ch. 16.4 - Prob. 45E Ch. 16.4 - Prob. 46E Ch. 16.4 - Prob. 47E Ch. 16.4 - Prob. 48E Ch. 16.4 - Prob. 49E Ch. 16.4 - Prob. 50E Ch. 16.4 - Prob. 51E Ch. 16.4 - Prob. 52E Ch. 16.4 - Prob. 53E Ch. 16.4 - Prob. 54E Ch. 16.4 - Prob. 55E Ch. 16.4 - Prob. 56E Ch. 16.4 - Prob. 57E Ch. 16.4 - Prob. 58E Ch. 16.4 - Prob. 59E Ch. 16.4 - Prob. 60E Ch. 16.5 - Prob. 1PQ Ch. 16.5 - Prob. 2PQ Ch. 16.5 - Prob. 3PQ Ch. 16.5 - Prob. 1E Ch. 16.5 - Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Prob. 37E Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 44E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Prob. 47E Ch. 16.5 - Prob. 48E Ch. 16.5 - Prob. 49E Ch. 16.5 - Prob. 50E Ch. 16.5 - Prob. 51E Ch. 16.5 - Prob. 52E Ch. 16.5 - Prob. 53E Ch. 16.5 - Prob. 54E Ch. 16.5 - Prob. 55E Ch. 16.5 - Prob. 56E Ch. 16.5 - Prob. 57E Ch. 16.5 - Prob. 58E Ch. 16.5 - Prob. 59E Ch. 16.5 - Prob. 60E Ch. 16.5 - Prob. 61E Ch. 16.5 - Prob. 62E Ch. 16.5 - Prob. 63E Ch. 16.5 - Prob. 64E Ch. 16.5 - Prob. 65E Ch. 16.5 - Prob. 66E Ch. 16.6 - Prob. 1PQ Ch. 16.6 - Prob. 2PQ Ch. 16.6 - Prob. 3PQ Ch. 16.6 - Prob. 4PQ Ch. 16.6 - Prob. 1E Ch. 16.6 - Prob. 2E Ch. 16.6 - Prob. 3E Ch. 16.6 - Prob. 4E Ch. 16.6 - Prob. 5E Ch. 16.6 - Prob. 6E Ch. 16.6 - Prob. 7E Ch. 16.6 - Prob. 8E Ch. 16.6 - Prob. 9E Ch. 16.6 - Prob. 10E Ch. 16.6 - Prob. 11E Ch. 16.6 - Prob. 12E Ch. 16.6 - Prob. 13E Ch. 16.6 - Prob. 14E Ch. 16.6 - Prob. 15E Ch. 16.6 - Prob. 16E Ch. 16.6 - Prob. 17E Ch. 16.6 - Prob. 18E Ch. 16.6 - Prob. 19E Ch. 16.6 - Prob. 20E Ch. 16.6 - Prob. 21E Ch. 16.6 - Prob. 22E Ch. 16.6 - Prob. 23E Ch. 16.6 - Prob. 24E Ch. 16.6 - Prob. 25E Ch. 16.6 - Prob. 26E Ch. 16.6 - Prob. 27E Ch. 16.6 - Prob. 28E Ch. 16.6 - Prob. 29E Ch. 16.6 - Prob. 30E Ch. 16.6 - Prob. 31E Ch. 16.6 - Prob. 32E Ch. 16.6 - Prob. 33E Ch. 16.6 - Prob. 34E Ch. 16.6 - Prob. 35E Ch. 16.6 - Prob. 36E Ch. 16.6 - Prob. 37E Ch. 16.6 - Prob. 38E Ch. 16.6 - Prob. 39E Ch. 16.6 - Prob. 40E Ch. 16.6 - Prob. 41E Ch. 16.6 - Prob. 42E Ch. 16.6 - Prob. 43E Ch. 16.6 - Prob. 44E Ch. 16.6 - Prob. 45E Ch. 16.6 - Prob. 46E Ch. 16.6 - Prob. 47E Ch. 16.6 - Prob. 48E Ch. 16.6 - Prob. 49E Ch. 16.6 - Prob. 50E Ch. 16.6 - Prob. 51E Ch. 16.6 - Prob. 52E Ch. 16 - Prob. 1CRE Ch. 16 - Prob. 2CRE Ch. 16 - Prob. 3CRE Ch. 16 - Prob. 4CRE Ch. 16 - Prob. 5CRE Ch. 16 - Prob. 6CRE Ch. 16 - Prob. 7CRE Ch. 16 - Prob. 8CRE Ch. 16 - Prob. 9CRE Ch. 16 - Prob. 10CRE Ch. 16 - Prob. 11CRE Ch. 16 - Prob. 12CRE Ch. 16 - Prob. 13CRE Ch. 16 - Prob. 14CRE Ch. 16 - Prob. 15CRE Ch. 16 - Prob. 16CRE Ch. 16 - Prob. 17CRE Ch. 16 - Prob. 18CRE Ch. 16 - Prob. 19CRE Ch. 16 - Prob. 20CRE Ch. 16 - Prob. 21CRE Ch. 16 - Prob. 22CRE Ch. 16 - Prob. 23CRE Ch. 16 - Prob. 24CRE Ch. 16 - Prob. 25CRE Ch. 16 - Prob. 26CRE Ch. 16 - Prob. 27CRE Ch. 16 - Prob. 28CRE Ch. 16 - Prob. 29CRE Ch. 16 - Prob. 30CRE Ch. 16 - Prob. 31CRE Ch. 16 - Prob. 32CRE Ch. 16 - Prob. 33CRE Ch. 16 - Prob. 34CRE Ch. 16 - Prob. 35CRE Ch. 16 - Prob. 36CRE Ch. 16 - Prob. 37CRE Ch. 16 - Prob. 38CRE Ch. 16 - Prob. 39CRE Ch. 16 - Prob. 40CRE Ch. 16 - Prob. 41CRE Ch. 16 - Prob. 42CRE Ch. 16 - Prob. 43CRE Ch. 16 - Prob. 44CRE Ch. 16 - Prob. 45CRE Ch. 16 - Prob. 46CRE Ch. 16 - Prob. 47CRE Ch. 16 - Prob. 48CRE Ch. 16 - Prob. 49CRE Ch. 16 - Prob. 50CRE Ch. 16 - Prob. 51CRE Ch. 16 - Prob. 52CRE Ch. 16 - Prob. 53CRE Ch. 16 - Prob. 54CRE Ch. 16 - Prob. 55CRE Ch. 16 - Prob. 56CRE Ch. 16 - Prob. 57CRE Ch. 16 - Prob. 58CRE Ch. 16 - Prob. 59CRE Ch. 16 - Prob. 60CRE Ch. 16 - Prob. 61CRE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

A sketch of the region of integration ∫ 0 5 ∫ 0 y x d x d y and evaluate by changing to polar coordinates.

Solution Summary: The author evaluates the region of integration by changing to polar coordinates.

Concept explainers

Videos

A sketch of the region of integration $\int_{0}^{5} \int_{0}^{y} x d x d y$ and evaluate by changing to polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

A sketch of the region of integration ∫ 0 5 ∫ 0 y x d x d y and evaluate by changing to polar coordinates.

Solution Summary: The author evaluates the region of integration by changing to polar coordinates.

Concept explainers

Videos

A sketch of the region of integration ∫05∫0yx dx dy and evaluate by changing to polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

A sketch of the region of integration $\int_{0}^{5} \int_{0}^{y} x d x d y$ and evaluate by changing to polar coordinates.