# Thread: 298 AP Calculus Exam int of e

1. calculator returned this but know sure why
$\displaystyle2 \int _1^2e^udu$

note there might be a duplicat of this post ???  Reply With Quote

2.

3. $u=\sqrt{x} \implies du = \dfrac{1}{2\sqrt{x}} \, dx$

$\displaystyle {\color{red}{2}} \int_1^4 \frac{e^{\sqrt{x}}}{{\color{red}{2}} \sqrt{x}} \, dx = 2 \int_1^2 e^u \, du$  Reply With Quote Originally Posted by skeeter $u=\sqrt{x} \implies du = \dfrac{1}{2\sqrt{x}} \, dx$

$\displaystyle {\color{red}{2}} \int_1^4 \frac{e^{\sqrt{x}}}{{\color{red}{2}} \sqrt{x}} \, dx = 2 \int_1^2 e^u \, du$
Why would that change the limits,?  Reply With Quote

5. Originally Posted by karush Why would that change the limits,?
The original integral over x was done over an interval (1, 4).

When we changed the variable to u(x) we are no longer integrating over x. We are now integrating over u. So the interval changes to (1, 2).

-Dan  Reply With Quote

6. When you change from x to u, every reference to "x" has to change to a reference to "u". "$\displaystyle \int_1^4 dx$" means we are taking the integral fron x= 1 to x= 4. We have to change that to u. When x= 1, $\displaystyle u= \sqrt{1}= 1$ and when x= 4, $\displaystyle u= \sqrt{4}= 2$.  Reply With Quote

+ Reply to Thread \$displaystyle2, 298, calculator, int, returned #### Posting Permissions 