Question

find the shared area between curves
y=2 sin(x), y=e^(4 x), x=0, x=pi/2

Answer 1

i would first make a rough picture of the graph of both functions together
and would look for the top function and the bottom function and do
\[\int\limits_{0}^{\frac{\pi}{2}}( Top-Bottom)dx\]

Answer 2

thats what i did

Answer 3

ok give me just a sec and i will do it for you and scan

Answer 4

so it is obvious e^(4x) is above 2sin(x) lol

Answer 5

so we have
\[\frac{1}{4}e^{\frac{\pi}{2}}-\frac{1}{4}-2=\frac{1}{4}e^\frac{\pi}{2}-\frac{1}{4}-\frac{8}{4}\]
\[=\frac{1}{4}e^\frac{\pi}{2}-\frac{9}{4}\]

Answer 6

is that what you got?

Answer 7

i;m gonna watch tv now

Answer 8

thanks, but you missed one number, it not pi/2, its 2pi

Answer 9

yea you are right it should be 1/4*e^(2pi)-9/4