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Chapter 5: Q. 43 (page 465)

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�13-x2dx

Short Answer

Expert verified

The solution of the integral issin-13x3+C.

Step by step solution

01

Step 1. Given Information.

The given integral is鈭�13-x2dx.

02

Step 2. Solve. 

To solve the integral, let x=3sinu, so derivation of uis dx=3cosudu.

Thus, substitute u into the original integral,

鈭�13-x2dx=鈭�13-3sinu23cosudu=鈭�131-sin2u3cosuduLet'susetheidentitysin2x+cos2x=1=鈭�1cos2ucosudu=鈭�1du=u+C

Substitute back uin the above equation,

=sin-13x3+C

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