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Chapter 4: Q. 31 (page 362)

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess-and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.

鈭�4ex-32dx

Short Answer

Expert verified

The solution of the integral is2e2x-6+C.

Step by step solution

01

Step 1. Given Information.

The given integral is鈭�4ex-32dx.

02

Step 2. Solve. 

By solving the integral we get,

鈭�4ex-32dx=鈭�4e2x-6dx=4鈭�e2x-6dxUse鈭�exdx=ex+C=412e2x-6+C=2e2x-6+C

03

Step 3. Verification. 

To verify the answer we differentiate 2e2x-6+Cit.

On differentiating we get,

2e2x-6+C=ddx2e2x-6+ddxC=4e2x-6+0=4e2x-6

Hence proved.

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Most popular questions from this chapter

Show that F(x)=sinx-xcosx+2 is an antiderivative of f(x)=sinx.

Determine which of the limit of sums in Exercises 47鈥�52 are infinite and which are finite. For each limit of sums that is finite, compute its value

limn鈫�鈭�鈭�k=1nk3n4+n+1

Properties of addition: State the associative law for addition, the commutative law for addition, and the distributive law for multiplication over addition of real numbers. (You may have to think back to a previous algebra course.)

Compare the definitions of the definite and indefinite integrals. List at least three things that are different about these mathematical objects.

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�鈭�32鈥�1x+5dx
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