Find the area between the curve f(x) =sinx and g(x) = cosx over the interval x=-2 and x=5

Q: integral

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Q: 8. Find the area bounded by x² – 6x + y = 0, - x² – 2x – y = 0, and the x – axis.

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Q: What is the area under the curve f(x) = sinx over the interval [0, pi/2]

A: First:                  Let's draw the graph of the curve f(x)=sin x  over the interval: [0, π2]…

Q: Find the area of the region between the curves y = sin(x), y = sin(2x), x = 0, and x = t/2. Area…

A: Given curve is : y=sinx   .......(1) y=sin2x   ......(2) To find the area of region between curve…

Q: Estimate the area under the graph of f(x) = 10 cos(x) from x = 0 to x = π/2 using four approximating…

A: Given that f(x) = 10cos(x)To find the area under the graph of f(x) from x = 0 to x = ?/2 using four…

Q: Estimate the area under the graph of x) - 5 cos(x) from xO to xR/2 using four approximating…

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Q: Find the area under the curve y=f(x)=x^3 from x=1 to x=3 using inscribed and circumscribed…

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Q: Find the area under the curve f(x) = sin x bounded by x ∈ [0, 3]

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: use a definite intergal to find the area under the curve between the give x-values. f(x)=2ex from…

A: Given data: f(x)=2ex from x=0 to x=ln4

Q: Find the area under the curve y = over the interval [1, 3 -

A: Given y=3xwe can use integration to find area under the curveArea=∫133xdx

Q: Make a sketch to show a case in which the area bounded by two curves is most easily found by…

A: To graph: The sketch to show a case in which the area bounded by the two curves is most easily found…

Q: Find the area between the given curves: f(x) = sinx g(x) = cosx on the interval (0, π)

A: Sketch the region bounded by the curves fx=sinx  and  gx=cosx   on 0, π as shown below.

Q: ) Find the area bounded by Y,=cos(x) Y,= sin(x) X-0 and X-IT/2 graph it and show

A: Find the point of intersection of 2 curves.

Q: Solve the area bounded by the curve y=5-x^2 and the line y=2x. With graph.

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Q: Find the survace area of revolution about the x-axis of y= 4sin(2x) over the interval x is greater…

A: Given: The curve y=4sin2x for 0≤x≤π2 To find: Surface area of revolution of given curve about…

Q: Evaluate the definite integral using (a) the given integration limits and (b) the limits obtained by…

A: Evaluating the integral using (a) The given integration limits: We solve it by using u-v method:…

Q: Find the area between the furve f(x) =sinx and g(x) = cosx over the interval [90. 360] y=4x+16 x=--2…

A: Dear as per company guidelines we can answer only one question at a time, kindly post other question…

Q: sin(z)

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Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Evaluate the integral. (Use C for the constant of integration.) 11 tan“(x) sec (x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) (tan²(x) tan^(x) dx

A: Given       I=∫7tan2x++tan4xdx      = 7∫tan2x1+tan2xdx      = 7∫tan2x.sec2x dx∵sec2x-tan2x=1

Q: Find the area between the curves y = cos(x) and y = sin(x)  from x = -3π/4 to x = π/4. Draw the…

A: To find the area between the curves.

Q: When we find the area between an upper curve f(x) and a lower curve g(x), we integrate f(x)-g(x).…

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Q: Find the area between the curves. y = x5 - 2 ln (x + 5), y = x3 - 2 ln (x + 5)

A: Given: y=x5-2lnx+5y=x3-2lnx+5

Q: Find the area bounded by y = sin²(x) and y = sin³ (x) from< xS n.

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Q: Use a definite integral to find the area of the region between the curve y = 16x and the x-axis on…

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Q: Use the method of anti-derivative to find the area under the curve y = 4(x³ the interval [2,4]. 4x)…

A: Before finding the area, first, we will find the x-intercepts of the curve  to check that any point…

Q: Find the area bounded by y = sin²(x) and y = sin5(x) from 0 < x<

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Q: Find the area under the curve y = sin √x /√x between x = π^2/4 and x = π^2

A: Given function

Q: Use a definite integral to find the area of the region between the curve y = 17x and the xX-axis on…

A: Area is the double integral with respect to y and x. It is known that at x-axis that is y=0. We have…

Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

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Q: Find the area under the curve f(x)=6 , bounded by the x-axis,x=1 and x=3

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Q: What is the area under the curve y = cosx over the interval [0 ,π/2]?

A: Integrating the equation of curve in the given interval gives the area

Q: Find the area between the curve ​f(x)=x^2​+15 and the​ x-axis from x=3 to x=5.

A: Given query is to find the area under the curve.

Q: Find the area under the curve f(x) = 4 – ÷x² over the interval [0, 3] by using definition with x is…

A: Here we have to use application of Riemann Sum.

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: Use integration by parts to prove the reductionformula.

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Q: Find the area between the graphs of f(x)=sinx and g(x)=cosx for <x< 4

A: Graph of area from π4to5π4 is shown below÷ Red curve = sin(x) Blue cuve = cos(x)

Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: Find the area bounded by y = 0.5(x- 2)² – 1 and the X-axis from x-3 to x-5. Show the sketch with…

A: y= 0.5(x-2)2-10 =0.5(x-2)2-11 = 0.5 (x-2)22 = (x-2)2x - 2 = ± 2x =2+2    x~ 3.414orx =2-2x ~ 0.586

Q: y = sin(x), y = 2x

A:

Q: Find the area under y = 3 cos(x) and above y = 3 sin(x) for T < x < 2n. (Note that this area may not…

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Q: Use a definite integral to find the area of the region between the curve y = 3x and the x-axis on…

A:

Q: Find the area between the curve y = tan x and the x-axis from x = -π/4 to x = π/3

A: y=tanx from x=-π4 to x=π3. The graph is,

Q: make a sketch to show a case in which the area bounded by two curves is most eassily found by…

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Q: Calculate the area under the curve y between x = 2 and x 8. %3D

A: Since you have posted multiple questions therefore we will answer the first one for you. If you want…

Q: 5. Find the area under the curve integrate 2/(9 - x ^ 2) dx

A: Given;           ∫29-x2 dx Take the constant out: ∫a.fx dx=a.∫fx dx           =2.∫19-x2 dx Apply…

Q: Find the area under the graph of f(x)= sin' 2x cos 2x on the interval [0, 4).

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Q: find the area between the curves: f(x) = x2  + 1,   g(x) = 3 - x   on the interval [0,3]

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Q: 3. Find the area between the curve y = 2sinx cos x and the x-axis within the interval [0,2π].

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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.