Thread: Trig substitution

How can we find the integral with the substitution ?

I know how to find the integral, but the limits become the same sin(0) = sin(pi) = 0.

What should I do in general when a given substitution makes upper bound = lower bound?

Originally Posted by Hardwork

How can we find the integral with the substitution ?

I know how to find the integral, but the limits become the same sin(0) = sin(pi) = 0.

What should I do in general when a given substitution makes upper bound = lower bound?

Using a different property, you can analyse the integrand as a function with period "pi", the (signed) area of which equals zero after each period.

Originally Posted by Hardwork

How can we find the integral with the substitution ?

I know how to find the integral, but the limits become the same sin(0) = sin(pi) = 0.

What should I do in general when a given substitution makes upper bound = lower bound?

Is...





... so that, no matter which 'substitution' You do, the integral is 0...

Kind regards

Okay. I do see how the integral is zero. I just want to know what to do in general when a substitution makes the limits the same.