Set up an integral that represents the arc length of the function g(x)=sinxg(x)=sin⁡x for the interval [0,4π] in the form ∫ba f(x) dx.

Q: Evaluate the integral. (Use C for the constant of integration.) 6 arctan(Vx) dx

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Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2for 2≤x≤6if you integrate with…

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Q: Evaluate the integral. (Use C for the constant of integration.) 13 tan (x) sec (x) dx

A:

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

A: ∫tan8xcos9xdx

Q: Evaluate the integral ſ sin x dx by the method of geometry.

A:

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

A: ∫tan8xcos9xdx

Q: r" (tan (x)) (In (cos(x))) dx

A: solve this integration by substitution. substitue                    ln(cos(x)) = t on solving

Q: Find the indefinite integral. (Use C for the constant of integration.) tan( 2 dx sec 20 20

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Q: Find the indefinite integral. (Use C for the constant of integration.) (4 cos x + 3 sin x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 V 1- sin(x) dx

A: Evaluating the indefinite integral

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos X dx 3 + sin x

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Q: Evaluate the integral. (Use C for the constant of integration.) cos3 sin2 dt

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Q: Find the value of the definite integrallo 2 cos ( x ) dx given that the antiderivative for the…

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Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2 for 2≤x≤6 if you integrate with…

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Q: Use the tabular method to find the indefinite integral. ∫(1 − x)(e−x + 1) dx

A: We multiply the integrand then integrate each part…

Q: Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx 0,

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 arctan(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) | tan (x) cos°(x) dx

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Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

Q: Use the tabular method to find the integral. (Use C for the constant of integration.) 3x3 sin(x) dx

A: The given integral is ∫3x3sin x dx. ∫3x3sin x dx=3∫x3 sin x dx ddxxn=nxn-1∫sin xdx=-cos x+C∫cos…

Q: Set up an integral that represents the arc length of the function y = 4x4 + 5x from the point (0,0)…

A: We have to find a, b and f(x)

Q: Evaluate the integral. (Use C for the constant of integration.) (arctan(x))5 | x2 + 1 dx

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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. TC cos(x) sinh(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: Evaluate the integral. (Use C for the constant of integration.) fu- (x – 3)sin(Tx) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 10 sin(2x) dx 1 + cos“(x)

A: Answer is -10arctan(cos^2x)+C.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin20(x) dx

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Q: What is the integral of sin^5 x cos^3 x dx if the lower limit is zero and the upper limit is T/2?

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Q: Find the indefinite integral. ∫arctan x dx

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Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan*(x) sec (x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) tan (x) cos7(x) dx

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Q: Evaluate the integral. (Use C for the constant of integration.) sin (x) cos (x) dx 4.

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Q: Set up an integral that represents the arc length of the curve y 2xi from the point (0, 0) to (2,…

A: our objective is to setup the arc length formula

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

A: Given,            ∫7tan xlncos x dx

Q: Set up an integral that (if solved) would give the arc-length of the following curve on the given…

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Q: S tanʼx dx

A: Answer is given in next step.

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos5(x) sin*(x) dx

A:

Q: Find the indefinite integral. ∫4 arccos x dx

A: To evaluate the integral: ∫4cos-1x dx Integration by parts states that: ddxuv=v·ddxu-∫ddxv∫udxdx…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x)/sin^20(x)    dx

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

A:

Q: Evaluate the definite integral.

A: ∫012arccosx1-x2 dx Consider, ∫arccosx1-x2 dx Now put, arccosx=t⇒-11-x2=dtdx⇒11-x2 dx=-dt Therefore,…

Q: Set up the integral for the arc lengthof the function,y=43x32for 2≤x≤6if you integrate with respect…

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 tan(x)sec^3(x)dx

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Q: Consider the curve given by f( x ) = 4 cos( 2.5 x) on the interval 0 sxs 2 n. 4 1 -1 -2 -3 -4 1 4 6.…

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Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin(2x) dx 1 + cos“(x)

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Q: Set up the definite integrals to compute the arc length and the surface area formed by rotating the…

A: The function is f(x)=4-x2 and the interval is [-2, 2] Equation of line is x=3.   To find: The arc…

Q: The definite integral that can be used to find the arc length of the curve y =x-2 on the interval…

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Q: (a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

A:

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 this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

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.