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Solve given definite integral.

11x39x21dx

Short Answer

Expert verified

0

Step by step solution

01

Step1. Given Information

The integral is as follows.

11x39x21dx

The objective is to solve the integral.

02

Step2. Assumptions

To solve the integral, let u=x2

Now, derivation of above equation is solved below.

u=x2du=2xdx

03

Step3. Solution

The integral is solved below.

x39x21dx=u29u1du=12u9u1du

=1229v2v29+19dvv=9u1,dv=929u1dx

=19v29v2+1dv

=181v4+v2dv

=181v4dv+181v2dv

=1405(v)5+1243(v)3

=1405(9u1)5+1243(9u1)3

=14059x215+12439x213

=x245+212159x2132

04

Step4. Solution

The definite integral is solved below.

11x39x21dx

=x245+212159x213211

=1245+212159(1)2132(1)245+212159(1)2132

=0

Therefore, the value is 0

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