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Solve given definite integral.

04x3x2+4dx

Short Answer

Expert verified

242.78

Step by step solution

01

Step1. Given Information

The integral is as follows.

04x3x2+4dx

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.

x3x2+4dx=u2u+4du=12uu+4du

=122v2v24dvv=u+4,dv=92u+4du

=v44v2dv=v4dv4v2dv=15(v)543(v)3

=15x2+45243x2+432

=x25815x2+432

04

Step4. Solution

The definite integral is solved below.

04x3x2+4dx

=x25815x2+43204

=42581542+43202581502+432

=32053+6415

=242.78

Therefore, the value is242.78

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