(t³ + t)dt

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

A:

Q: In Exercises 1-6, evaluate the integral using the Integration by Parts formula with the given choice…

A: Given, ∫tan-1x dx To find the integral of the given function, By using the integration By Parts…

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: Consider the function g (x) = S (2tª – 3t – 8) dt. Evaluate the integral using the Fundamental…

A:

Q: In Exercises 5-40, determine whether the improper integral convergesand, if so, evaluate it.

A: To determine whether the improper integral converges ∫0∞1x+13dx

Q: In Exercises 25-28, sketch the domain of integration and express as an iterated integral in the…

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: 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.

A:

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: 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 5-40, determine whether the improper integral convergesand, if so, evaluate it.

A: Given integral is ∫561(x-5)3/2dx.

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

A:

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

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

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

A:

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 5-40, determine whether the improper integral convergesand, if so, evaluate it.

A: Given information: ∫36xx-3dx

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 5-40, determine whether the improper integral convergesand, if so, evaluate it.

A: Consider the given improper integral, ∫01lnxdx since the function is not defined at lower limit we…

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

A:

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

A: we have to integrate ∫03dxx2+3

Q: In Exercises 25-28, evaluate the integral in the form a sin(u(x)) + C foran appropriate choice of…

A: Evaluate: ∫ x3 cosx4 dx

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 1-6, evaluate the integral using the Integration by Parts formula with the given choice…

A:

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 5-40, determine whether the improper integral convergesand, if so, evaluate it.

A: Given: ∫1∞dxx2019

Q: In Exercises 5-40, determine whether the improper integral convergesand, if so, evaluate it.

A: The given integral is I=∫-∞0x2exdx