Between the sine and inverse sine Find the area of the region bounded by the curves y = sin x and y = sin-1x on the interval [0, 1/2].

Q: Find the area of the region enclosed by the tangent line of the function f(x) at x = 2 and the…

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Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: Consider the given function ∫23x33-x-x3dx First, draw the graph of the first function y=x33-xand…

Q: Consider the rose curve given by r = 3 cos 30 shown in the figure below (note that the 0-values in…

A: we will find the integration of one loop of rose curve and multiply it by 3, since all three loops…

Q: cos' x+cos'x dx is sin x+sin'x Q 9. The value of the integral

A: Introduction :

Q: 18. Find relative extrema of f(x) = sin where function is increasing. cos x, over the interval , .…

A: Given fx=sinx2cosx We have to find the relative extrema of fx=sinx2cosx over the interval -π2, π2.…

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Given Data: The expression to calculate the area under the curve is, The expression to find the…

Q: " cos Inx dx Evaluate the Integral A - sin Inx + C B sin Inx + C cos Inx + C sin Inx D - + C

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Q: f(x)= (1-cos x)/sinx +(sin x)/(1-cos x) find its integral

A: To find the integral  ∫1-cosxsinx+sinx1-cosxdx

Q: Find the indefinite integral. (Use C for the constant of integration.) 17 tan(x) ln cos(x) dx

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Q: 7 sin (x) cos (x) dx

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: To find:

Q: 3n/2 tan x The value of integral dx tan x + cot x

A: Let I is the value of given Integral.

Q: The diagram below shows the curve with equation sin 0 <I< 2n. The shaded area A is the area under…

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Q: Find the area of the region that lies inside the first curve and outside the second curve Note: show…

A: The given curves are: r=2+sinθ         and        r=3sinθ

Q: Evaluate the integral using Trigonometric Integrals S (8 – - 3cos (x)sin°(x) dx °(x)sin´(x)dx

A: We can find the integration as below using trigonometric integral.

Q: VI– 2e* dx

A: Given that a integration and we solve the solution of this integration by using general property of…

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

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Q: Integrals of cot x and csc x Use a change of variables to prove that  ∫ cot x dx = ln | sin x | + C.

A: prove that ∫cotxdx=lnsinx+c we know that cotx=cosxsinx

Q: 3 sin 0 and outside the curve 5. Find the area of the region that lies inside the curve r = r = 2 –…

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: Given that a integration and we solve it by using general formulas of integration. We know that…

Q: x cos(x dx esin(x2) Find the indefinite integral

A: To find the indefinite integral∫x cos (x2)esin (x2)dxFormula:ddx(xk)=kxk-1ddx sin x= cos x∫exdx=ex+C

Q: sin x + cos r dr

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Q: The plot below shows a portion of the graph of r = 2 - sin 0 in polar coördinates. Please find the…

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Q: Determine the integral by trigonometric substitution: ∫√x^2-15 / x^3  dx

A: Given. ∫x2-15x3dx                               .........1 Let  x=15 secθ On differentiating.  dx=15…

Q: Review of Definite & Indefinite Integrals Evaluate the definite integral. sin(3t)dt

A: Integration of sin(at) = - (cos(at) / a) + C

Q: The integrand of the definite integral is a difference of two functions. Sketch the graph of each…

A: Topic = Application of integration

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: 5 – 5 sin(x) dx cos(x)

A: Please see the answer below

Q: Find the area of the curve r = sin (3θ) when 0<θ <π. Graph.

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Q: dz 1. + 6z + 5

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Write out the integral to find the area of the region that lies inside the curve r = 4 sin 0 and…

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Q: Integration of sin^2 x?

A: Cos(2x) = 1 - 2Sin2(x)  Sin2(x)=1 - Cos(2x)2   Integration of cos(x) is Sin(x)

Q: By using a graphing device, one can estimate that the points of intersection of the curves r = 3+…

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Q: Integral sign with 1/2 on top and 0 on bottom:  x cos Pi x   dx

A: To evaluate

Q: Ssin (x) + sin(x) cos²(x) To evaluate the dx using basic formula of integration (without using…

A: This question is based on indefinite integral.

Q: 27 Find the exact values of the expressions: (a) sin-' ( sin 3 -1 COS and (b) tan - sin -1 Find the…

A: Find the value of by using the fact that

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: Find ∫7tan2x secx dxw.k.t tan2x=sec2x-1∫7tan2x sec x dx=7∫sec2x-1=7∫sec3x-dx-∫secx dx

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Use left and right endpoints and the given number of rectangles to find two approximations of the…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.)   9 sin5(x) cos3(x) dx

A: ∫9sin5xcos3xdx We need to Evaluate the integral

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

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Q: Approximate the area under a curve using midpoint approximation Question Approximate the area under…

A: Given:

Q: 3. Find the area of the region bounded by the graphs of x = 3 - y? and y = x – 1. 4. The sine and…

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Q: aluate the definite integral. Use a graphing utility to verify your result. TT/4 x sin 2x dx

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Q: Using Simpson’s Rule with n=4 subintervals approximate the area under the sine curve f(x)=sinx…

A: . We need to find out the area under the given curve using Simpson's rule between the interval  x=0…

Q: π 6. tan 2x dx

A: ∫0π6tan 2x dx

Q: coS X Find the integral of cot x using the substitution cot x = sin x

A: Given : To determine∫cotxdx using substitution

Q: The integrand of the definite integral as attached is a difference of two functions. Sketch the…

A: Given that: The integral is ∫04 (x+1)-x2dx .

Q: COSX (25) Find the area between the curve y= and x-axis and x 1/2, x 1/6 sin x

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.