Evaluate the following integrals. Assume a and b are real

Cem Hayes

Cem Hayes

Answered question

2021-09-25

Evaluate the following integrals. Assume a and b are real numbers and n is a positive integer.
xax+bdx

Answer & Explanation

AGRFTr

AGRFTr

Skilled2021-09-26Added 95 answers

Step 1
Consider the integrals,
xax+bdx...(1)
Step 2
Let, ax+b=t2
To solve,
ax=t2b
x=t2ba
Differentiating   w.r.t.t
adx+o=2tdt
adx=2tdt
dx=2tadt
Step 3
Substitute x=t2baanddx=2tadt in equation (1)
then,
xax+bdx=1tt2ba2tadt
=2t(t2b)ta2dt
=2a2(t2b)dt
=2a2(t33bt)+C
=2a2[ax+b33bax+b]+C
=2a2[13(ax+b)32bax+b]+C
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-08Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?