# Thread: If int[pi/3,pi/2][sin(x)/(1+cos(x))]dx = int[3/2,1][f(u)]du, then what are "u", "du"?

1. ## If int[pi/3,pi/2][sin(x)/(1+cos(x))]dx = int[3/2,1][f(u)]du, then what are "u", "du"?

$\displaystyle \mbox{If }\, \int_{\pi/3}^{\pi/2}\, \dfrac{\sin(x)}{1\, +\, \cos(x)}\, dx\, =\, \int_{3/2}^1\, f(u)\, du,$

. . .$\mbox{then which of the following statements is true?}$

$\mbox{A. }\, u\, =\, 1\, +\, \cos(x),\, du\, =\, \sin(x)\, dx$

$\mbox{B. }\, u\, =\, 1\, +\, \cos(x),\, du\, =\, -\sin(x)\, dx$

$\mbox{C. }\, u\, =\, \cos(x),\, du\, =\, \sin(x)\, dx$

$\mbox{D. }\, u\, =\, \cos(x),\, du\, =\, -\sin(x)\, dx$

$\mbox{E. }\, u\, =\, \sin(x),\, du\, =\, \cos(x)\, dx$

The first thing I did was solve the left function getting ln(3/2) and then I thought the next step would be to solve f(u)du by subbing in the options being
1 + cosx, cosx, and sinx to find the integral but I can't get right side to = left side. Anybody know how to go about this?

2. Originally Posted by chriswu6
$\displaystyle \mbox{If }\, \int_{\pi/3}^{\pi/2}\, \dfrac{\sin(x)}{1\, +\, \cos(x)}\, dx\, =\, \int_{3/2}^1\, f(u)\, du,$

. . .$\mbox{then which of the following statements is true?}$

$\mbox{A. }\, u\, =\, 1\, +\, \cos(x),\, du\, =\, \sin(x)\, dx$

$\mbox{B. }\, u\, =\, 1\, +\, \cos(x),\, du\, =\, -\sin(x)\, dx$

$\mbox{C. }\, u\, =\, \cos(x),\, du\, =\, \sin(x)\, dx$

$\mbox{D. }\, u\, =\, \cos(x),\, du\, =\, -\sin(x)\, dx$

$\mbox{E. }\, u\, =\, \sin(x),\, du\, =\, \cos(x)\, dx$

The first thing I did was solve the left function getting ln(3/2)
What do you mean by "the left function"? What do you mean by "solving" it? How did you end up with a natural log? Please show your steps.

Originally Posted by chriswu6
and then I thought the next step would be to solve f(u)du by subbing in the options being
1 + cosx, cosx, and sinx to find the integral but I can't get right side to = left side. Anybody know how to go about this?
What did you get when you tried each of the answer options? Please show your work and results. Thank you!

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