Question

the area of the region bounded by lines x=0, x=2 and y=0 and the curve y=e^(x/2) is....
a)(e-1)/2
b)e-1
c)2(e-1)
d)2e-1
e)2e
please show me how to do this....

Answer 1

integrate y(x) on the interval 0-2

Answer 2

i know i need to do that but i dont know how to.

Answer 3

a u-sub is needed\[u=\frac x2\implies du=\frac{dx}2\]

Answer 4

where are you stuck?

Answer 5

rewrite your integral in terms of u and let us know where you get stuck

Answer 6

the derivative of e^x/2 is what confused me

Answer 7

d(e^u)/du=e^u

Answer 8

so when i write the integral it would be from 0 to 1 (e^u)du

Answer 9

oh with a 2 in front though?

Answer 10

if you want to evaluate it in terms of u, then yes

Answer 11

then i have to do what?

Answer 12

write down the answer...
there's nothing to do after you evaluate, that's the last step

Answer 13

i thought i have to integrate to get rid of the du?

Answer 14

yes, substitution, integration, then evaluation. you can either evaluate for u if you change intervals or plug x"s back in for u and then evaluate

Answer 15

\[2\int\limits_{0}^{1}e ^{u}du\]

Answer 16

thats what i have

Answer 17

now integrate

Answer 18

sooo id get... umm 2* idk.

Answer 19

i dont understand e's

Answer 20

the integral of e^u*du is e^u

Answer 21

evaluate for upper and lower limits of u or x

Answer 22

ohh okay, thanks

Answer 23

what do you get?

Answer 24

i got 2(e-1)

Answer 25

k