Finding a definite integral using a given substitution.

**dix** · May 29th 2011, 06:12 AM

Hi, I have been given this question and can only get so far, I'm having trouble with the last part. Any help is good thanks

**Prove It** · May 29th 2011, 06:17 AM

First of all, when you let $\displaystyle u = \sin{x} \implies du = \cos{x}\,dx$ , you also need to change the terminals.

$\displaystyle u(0) = 0$ and $\displaystyle u\left(\frac{\pi}{2}\right) = 1$ .

So $\displaystyle \int_0^{\frac{\pi}{2}}{2\cos{x}\,e^{\sin{x}}\,dx} = \int_0^1{2e^u\,du} = \left[2e^u\right]_0^1$

Go from here.

**dix** · May 29th 2011, 06:45 AM

Thanks Prove It.

I don't understand how $\displaystyle u(0) = 0$ and $\displaystyle u\left(\frac{\pi}{2}\right) = 1$ .

What does $\displaystyle u\left(\frac{\pi}{2}\right) = 1$ mean? Do you substitute $(\frac{\pi}{2}\right)$ somewhere?

**bugatti79** · May 29th 2011, 06:51 AM

Originally Posted by dix

Thanks Prove It.

I don't understand how $\displaystyle u(0) = 0$ and $\displaystyle u\left(\frac{\pi}{2}\right) = 1$ .

What does $\displaystyle u\left(\frac{\pi}{2}\right) = 1$ mean? Do you substitute $(\frac{\pi}{2}\right)$ somewhere?

Yes, note that $\displaystyle u(0) = 0$ is the same as writing when x =0 (ie the zero in the bracket) then u = 0 because we know that u = sin x. Same idea for the upper limit.

**dix** · May 29th 2011, 07:03 AM

Oh right, thanks. I had my calculator in degrees instead of radians so it came out different.

I'm supposed to end up with 2(e-1), could you tell me where i've went wrong here?

**Prove It** · May 29th 2011, 07:13 AM

You are evaluating $\displaystyle \left[2e^u\right]_0^1$ , not $\displaystyle \left[2e^{\sin{x}}\right]_0^1$ . The whole point in changing your terminals when you make the substitution is so that you DON'T have to convert the integral back to a function of $\displaystyle x$ .

**dix** · May 29th 2011, 07:50 AM

Oh right. Thanks again.

Thread: Finding a definite integral using a given substitution.

LinkBack

Thread Tools

Display

Finding a definite integral using a given substitution.

Similar Math Help Forum Discussions

[SOLVED] Definite Integral By Substitution

[SOLVED] Hard (or maybe it's not?) u-substitution definite integral problem

(probably) Easy U-substitution definite integral problem?

Find the definite integral using substitution

Definite integral substitution???

Search Tags