back-substituting is not an efficient method of solving these problems. You should also change the limits of the integral as well.

so the substitution

will change

to

as when

and when

.

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Here is another question that examiners/universities love to ask on this topic.

Could you explain the following error in my working.

I wish to solve the integral

Using the substitution

the limits stay the same because

at

so the integral becomes

so

therefore

however

so the integral cannot be equal to zero.

So where did I go wrong?

P.S. the question is for Mathstud28 no other takers please.

Bobak