1/2 cos' x sin x dx 3

Q: In Exercises 29-76, evaluate the indefinite integral.

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Q: In Exercises 5-40, evaluate the integral using FTC I.

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Q: In Exercises 5-40, evaluate the integral using FTC I.

A: Given: ∫0π3cost dt

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

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Q: In Exercises 85-98, use the Change of Variables Formula to evaluate thedefinite integral.

A: Given:∫1017x-9-23 dxIntegrating formula:∫xn dx=xn+1n+1

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

A: ∫cosx5-2sinxdx∫u*vdx=u∫vdx-∫[ddx(u)∫vdx]dx∫sinx dx=-cosx+c∫cosx dx=sinx+c

Q: Verify the integration formulas in Exercises 37-40. / In(1 - x) + c 40. tanhx dx = x tanhx +

A: Consider, ddxx tanh-1x+12ln1-x2+C=dx…

Q: Evaluate the integrals in Exercises 9– 18 It may be necessary to use a substitution first. x dx 9.…

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

Q: In Exercises 85-98, use the Change of Variables Formula to evaluate thedefinite integral.

A: The given integral is ∫0e-1x3x2+1dx.

Q: In Exercises 1-10, indicate a good method for evaluating the integral (butdo not evaluate). Your…

A: Let the integral be y - y = ∫xsec2x dx                             .......................(1)Using…

Q: In Exercises 29-76, evaluate the indefinite integral.

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Q: In Exercises 49-54, evaluate the integral in terms of the constants.

A: We have to evaluate ∫-xxt3+1dt From Property of definite integral, we have ∫-aafxdx=2∫afxdx…

Q: In Exercises 5-40, evaluate the integral using FTC I.

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Q: Find the exact value of the arc length of each function f(x) in Exercises 31-46 on [a, b] by writing…

A: Given: The function fx=3x+1 over the interval a,b=-1,4, To determine: The arc length of the function…

Q: In Exercises 15-34, calculate the integral.

A: We have to calculate integral ∫12212dxx16x2-1

Q: |In Exercises 67–70, use the following alternative method for evaluating the integral J = f sin" x…

A: Consider the given formulas:

Q: In Exercises 61-64, express each integral as a single integral.

A: The given integral is , ∫73fxdx+∫39fxdx To write the given integral in a single integral, applying…

Q: In Exercises 57-60, calculate the integral, assuming that f (x)dx = 1, f(x) dx = 4, f(x)dx = 7

A: Definite integral: Property of definite integral Reversing the limits of integration changes the…

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

A:

Q: In Exercises 55-58, calculate the integral, assuming that | S(x)dx = 1, f(x) dx = 4, f (x) dx = 7

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Q: In Exercises 10-37, evaluate the indefinite integral. Remember, there areno Product, Quotient, or…

A: To integrate: ∫x2-sec2xdx Evaluating the integral. ∫x2-sec2xdx=∫x2dx-∫sec2xdx=x33-tanx+C

Q: In Exercises 61-64, express each integral as a single integral.

A: The given integral is ∫03f(x)dx+∫37f(x)dx. Concept used: Property of integral:…

Q: In Exercises 7-24, write the integral in terms of u and du. Then evaluate.

A: It is given that,∫sinθ cos3θ dθ ,  u=cosθ. We have to write the integral in terms of u and du. Then…

Q: In Exercises 15-34, calculate the integral.

A: Our Aim is to calculate the integral given below:-I=∫dxxx4-1 -(i)

Q: In Exercises 5-40, evaluate the integral using FTC I.

A: ∫0π6secθtanθ dθ

Q: In Exercises 85-98, use the Change of Variables Formula to evaluate thedefinite integral.

A: Given: The definite integral is  ∫01θtan(θ2)dθ   To determine: The value of the definite integral…

Q: In Exercises 11-59, evaluate the integral using the appropriate methodor combination of methods…

A: ∫(3x2-1)x(x2-1)dx

Q: Calculate the gaussian integral, e- dx, using the complex integration [residue theorem]

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Q: In Exercises 29-76, evaluate the indefinite integral.

A:

Q: In Exercises 15-32, evaluate using trigonometric substitution. Refer to the table of trigonometric…

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