Question

Calculus II Area between curves homework

Sketch the region enclosed by the given curves.
Find its area.
y = 4 cos 4x, y = 4 - 4 cos 4x, from 0 to pi/4

I've sketched the graph, but I'm not sure how to calculate the exact point of intersection.
The intersection is (0.26179939, 2), but I don't know what that would be as a fraction.

Answer 1

you dont have to i don't think

Answer 2

from 0 to pi/4

Answer 3

they are telling you the limits of integration
so it is not a region enclosed by the two curve, which is probably what you did in another problem
just between those endpoints

Answer 4

oops i see the problem they switch places damn

Answer 5

Yep. There's a point where they cross, and I have to switch the upper and lower functions at that point. The website we do our homework on doesn't like decimals, though, so I have to use fractions to get exact answers.

Answer 6

think they intersect at \(\frac{\pi}{12}\)which is a drag`

Answer 7

it is easier to solve without the machine
\[4\cos(4x)=4-4\cos(4x)\\
8\cos(4x)=4\\
\cos(4x)=\frac{1}{2}\]

Answer 8

unfortunately that makes
\[\cos(4x)=\frac{\pi}{3}\]so \[x=\frac{\pi}{12}\]

Answer 9

Oh, so that's how you figure it out.
I've got it now. :)
Thank you so much!

Answer 10

yw