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Chapter 5: Q 28. (page 429)

Solve the integral: 鈭�xsinxdx

Short Answer

Expert verified

The required answer is-xcosx+sinx+c.

Step by step solution

01

Step 1. Given information. 

We have given integral is鈭�xsinxdx.

02

Step 2. Solve the integration by parts . 

We have,

u=xdu=dx

and

localid="1648636397500" dv=sinxdxv=鈭�sinxdxv=-cosx

The formula of integration by parts is localid="1648645366461" 鈭�udv=uv-鈭�vdu

鈭�xsinxdx=x(-cosx)-鈭�(-cosx)dx=-xcosx+鈭�cosx=-xcosx+sinx+c

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Most popular questions from this chapter

Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.

鈭�xx2+1dx

Solve given definite integral.

鈭�04鈥�x3x2+4dx

Why don鈥檛 we ever have cause to use the trigonometric substitution x=cosu?

Why is it okay to use a triangle without thinking about the unit circle when simplifying expressions that result from a trigonometric substitution withx=asinuor x=atanu? Why do we need to think about the unit circle after trigonometric substitution with x=asecu?

Problem Zero: Read the section and make your own summary of the material.
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