| f(x)dx + | f(x)dx

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

A:

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

A: It is given that, ∫01fxdx=1,  ∫02fxdx=4  and  ∫14fxdx=7

Q: In Exercises 35-44, use properties of the integral and the formulas in thesummary to calculate the…

A: The given integral ∫-a1x2+xdx   Property used:   ∫fx±gxdx=∫fxdx±∫gxdx

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

A:

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

A: We have to evaluate ∫tan-1x2x2+1dx Let substitute u=tan-1x ⇒dudx=ddxtan-1x⇒dudx=11+x2⇒du=11+x2dx…

Q: (x²-3x+1) dx

A: Given that ∫23x2-3x+1dxSolution :∫23x2-3x+1dxx33-3x22+x23333-3322+3-233-3222+2

Q: In Exercises 43-48, write the integral as a sum of integrals without absolute values and evaluate.

A: Given- ∫0πcos xdx To find- Evaluating the above integral using proper identities. Concept used- As…

Q: In Exercises 43–47, calculate the integral, assuming that f(x) dx = 5, g(x) dx = 12 %3|

A:

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

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

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

A: ∫abf(x) dx=-∫baf(x)dx∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx

Q: In Exercises 45–48, calculate the integral, assuming that •5 .5 f(x) dx = 5, 8(x)dx 12

A:

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 43-48, write the integral as a sum of integrals without absolute values and evaluate.

A: Given integral is, ∫03x2-1dx

Q: In Exercises 45–48, calculate the integral, assuming that •5 .5 f(x) dx = 5, 8(x)dx 12

A: Given: ∫05fxdx=5, ∫05gxdx=12 To evaluate: ∫052fx-13gxdx Solution: We know that, ∫fx+gxdx=∫fxdx+∫gxdx…

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 52-56, evaluate the integral using the formulas in the summary and Eq. (9).

A: given integral, ∫-13x3dxwe have to evaluate the given integral

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

A: we have to integrate ∫03dxx2+3

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

A:

Q: Exercise 1. Evaluate the integral dx 1+e2x

A: ∫11+e2xdx Apply u-substitution u=1+e2xdu=121+e2x· 2e2x…

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

A:

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 43-48, write the integral as a sum of integrals without absolute values and evaluate.

A: Write the integral as a sum of integrals without absolute values and evaluate.

Q: dx —3 (х-1)(х-2)

A: Given: ∫-331x-1x-2dx

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

A: The given integral is, I=∫2x2+x4x3+3x22dx Using the substitution method, let 4x3+3x2=t on…