Evaluate each of the following integrals. \int_{0}^{2}(x^{2}+2x-3)^{3}(4x+4)dx

Brittney Lord

Brittney Lord

Answered question

2021-06-03

Evaluate each of the following integrals.
02(x2+2x3)3(4x+4)dx

Answer & Explanation

Latisha Oneil

Latisha Oneil

Skilled2021-06-04Added 100 answers

Step 1
To evaluate each of the following integrals.
Step 2
Given that
02(x2+2x3)3(4x+4)dx
=024(x2+2x3)3(x+1)dx
Let x2+2x3=t
Then dtdx=2x+2
dt=2(x+1)dx
Also at x=0 we havet=3
At x=2 we have t=22+43=83=5
Hence we have
02(x2+2x3)3(4x+4)dx
=235t3dt
=2[t44]35=12[54(3)4]
=12[62581]=272
02(x2+2x3)3(4x+4)dx=272

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-19Added 2605 answers

Answer is given below (on video)

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