4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break this up into two separate regions.)

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

A:

Q: 2. The area bounded by y=3x+4 and the curve y=x2 is revolved about the line x =5.

A: 2) The area bounded by the given curves is:

Q: 1) Find the area bounded by curve y = xvx2 + 1 and the lines x = 0, x = 4 an %3D the x-axis.

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Q: Find the area under the curve from x = 0 to x = 1 of y = (x 4 + x)5 (4x 3 + 1).

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Q: If Ls is the sum of the approximating rectangles for the area under the curve y =| cos z from 87 to…

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Q: Find the area under 3 sin(x) and above y = 3 cos(x) for 0 < x < T. that this area may not be defined…

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Q: 2) Find the area of the region bounded by y = sin x and below by y = cos x from x =- to x = 5n/4.…

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Q: 1. Find the area in the second quadrant bounded by the curve 2x² + 4x +y = 0 using two methods

A:

Q: y =x, 4x + y =12

A: Let's find.

Q: 2. Determine the area under the curve y = on [0, 1].

A:

Q: Set up integrals To find the area of the regions between the curve of y=4 cos x and the x axis for 0…

A: The Solution is given below

Q: Find the area of the given region y = tanh 2x

A: Given curve and figure: y = tanh 2x

Q: 1. Determine the area bounded by curves y = -x² + 4x + 3 and y = −x³ + 7x² − 10x + 5 over the…

A: We have to find the area bounded by the curves.

Q: 1. Find the area bounded by the curves y – 2 = x² ,y = 6 and the y – axis ( in Quadrant I only), as…

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: 1. Find the area of the region bounded by the ves y = x³ – 5x + 6, y = 10 – 4x – 4x2 and the line x…

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Q: 2. Find the area bounded by y = ÷x' 3x and y = -4. - %3D 3,

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Q: If L2 is the sum of the approximating rectangles for the area under the curve y = | cos x| from 2n…

A: Solve the following using left end points approximation

Q: Compute the exact area under y=4x2, above the axis and between x=0, x=1.

A: We have to compute the exact area under the given curve   y=4x2 Between the interval  x=0  and…

Q: 2.2. Use numerical integration to approximate o So ysinxdydx over a rectangular region with…

A: Given integral is ∫01∫01ysinxdydx                 (1) Here f(x, y)=ysinx So f(xi, yj)=yjsinxi Since…

Q: 7 Find the area under the curve y = x over the interval [1, 5]

A: Please refer to the image below

Q: What is the area bound between the curve y= \x/2 and the x-axis between x =-3 and 4/2 - 2/3 3 x = 2?…

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Q: Find the area under y = 2 sin(x) + 2 cos(x) and above the x-axis from x = 0 to x = Tt/2. Leave your…

A: The given function is,

Q: 1. Find the area bounded by y = -x' - 3x and y =- 4. |

A: solve the following

Q: 2. Find the area between between x = 0 and x =9. y=√x-10 and y=0 10

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Q: 2 (F(x) + x³)dx = ? %3D -1

A: Given that the area under f(x) in [-1,2] is 10br2 So,

Q: 8. Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis.

A: We have to find volume of solid generated by revolution.

Q: Show that the region bounded by y = 2 cos x, y = sin x, 3/2 -1. x = 0, x =- has area 2

A:

Q: 1. Find the area of the region bounded by the curves y=sin X16 , y = 0, and x = 6 obtained by…

A: topic - Area bounded by curves

Q: Evaluate the definity integral  from 0-4 (x-3)(x-5)dx

A: Evaluate the integral ∫04x-3x-5 dx.

Q: Find the area of the region bounded by the graphs of the equations y = cos x, y = sin (x), x = and x…

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Q: 2. Find the area bounded by the curve y = x³ – 3x2 from x = 0 to x = 2. -

A:

Q: 1. Find the area under the curve y = 9- a2 over the interval[0, 3] using right end point…

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Q: 1. Find the area under the curve of y on the interval [1, 4).

A:

Q: 5 -over the interval [4, 7]. Find the area under the curve y = (3x + 1)? Enter the exact answer.…

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Q: 8. Find the area in the first quadrant bounded by x = 0 using the most y=x², y = 2-x and appropriate…

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Q: 1. Find the total area bounded by the curves y = sin (x), y = cos (x), x = 0, x = n. Graph curves.

A: Given curves are: y=sinxy=cosxx=π So the area between these curves are shown in diagram below: So,…

Q: 2 Set up the definite integral required to find the area of the region between the graph of y = 20 –…

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Q: 4. Find the area under the curve y = Vx +6 from x = -6 to x = 3. Give exact answer.

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Q: 9:(a): Find the area bounded by the curve y² = -x, the line y = x, and the line y= 2.

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Q: 2. Find the area of the region bounded by x = y² - 4 and x = 3y.

A: Given query is to find the area of the region bounded by x=y2-4 and x=3y. The rule for integration…

Q: Approximate the area under the curve y=f(x) between x=-1 and x=5 using Simpson's rule with n=6…

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Q: 3 Find the area under the curve y over the interval [3, 8] (4x + 2)?

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Q: 10. Find the area bounded by 2. Hhe curves y=8x-x²0ind y=3x

A: topic - area bounded by curves

Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: 2. y = ln x, y = 0, x = 0. Solve in two ways.

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Q: Find the area under the curve for y = 3x over the interval [2,5).

A: The given curve is y=3x2

Q: 3 2. Find the area bounded by the two curves y = x³- 6x² + 8x and y = x² - 4x.

A:

Q: 5. Find the area of the region between the functions y= secx and y = tan x from x = 0 to x=- 2

A: The given curves are, y=secxy=tanx The limits are x=0 to x=π2. Then, the area is, I=∫0π2secx-tanxdx…

Q: 9) Find the area bounded under the curve y = x+2 and y=x² – 4.

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.