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Chapter 4: Q. 36 (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�(sin2x+cos2x)dx

Short Answer

Expert verified

The solution of the integral is x+C.

Step by step solution

01

Step 1. Given Information. 

The given integral is鈭�(sin2x+cos2x)dx.

02

Step 2. Solve. 

By solving the integral we get,

鈭�(sin2x+cos2x)dx=鈭�1dxsin2x+cos2x=1=x+C

03

Step 3. Verification. 

To verify the answer we differentiate x+Cit.

On differentiating we get,

x+C=ddxx+ddxC=1+0=1=sin2x+cos2xsin2x+cos2x=1

Hence proved.

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Most popular questions from this chapter

Explain why we call the collection of antiderivatives of a function f a family. How are the antiderivatives of a function related?

Use a sentence to describe what the notation鈭�k=2100k means. (Hint: Start with 鈥淭he sum of....鈥�)

Suppose f is a function whose average value on

[-2,5]is 10and whose average rate of change on

the same interval is -3. Sketch a possible graph for f .

Illustrate the average value and the average rate of change

on your graph of f.

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.)

Explain why the formula for the integral of xkdoes not

apply whenk=-1. What is the integral of x-1?
See all solutions

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