Question

Can someone help out, much appreciated

Answer 1

Just a sec

Answer 2

I am to find the area of regions R + S between the curves \(f(x)=cos(x)\) and \(g(x)=\frac{x+1}{3}\),




I'm stumped in finding region S. For region R, I did this:

\( \int_{-3.638}^{-1.862}\left(g\left(x\right)-f\left(x\right)\right)dx = 0.3981\)

Answer 3

I'm stumped on finding region S because how do I find it? It's across 3 quadrants so do I cut it into pieces and integrate one piece with respect to y and another with respect to x?

Also pls check if I did region R correct


@myeyeshurt

Answer 4

@mhchen

Answer 5

uh is there a picture

Answer 6

Just a sec

Answer 7

I would first find where they intersect each other (3 intersection points)

Answer 8

Yeah that's to find the upper and lower limits, and I know how to do that. But my question is, since the region is in 3 quadrants, do I need to integrate it with respect to y and divide the region into parts?

Answer 9

I'll just subtract the upper line and the lower line.

Answer 10

So I do not need to integrate with respect to y or break the region into parts? Maybe I'm thinking too hard for no reason, it is quite late I suppose

Answer 11

I think you can, but I'm thinking about it in a different way

Answer 12

ok

Answer 13

can you understand this

Answer 14

Yeah I get that. So you are saying that I find the area under cos x and the area under the linear function, and find what's in the middle?

Answer 15

smart

Answer 16

The area under the cosine minus the area under the linear thing is equal to the area between them is what I'm saying.

Answer 17

yeah I got you

Answer 18

so you gotta know where they intersect so you switch the top and bottom functions

Answer 19

yeah yeah wow thanks man (:

Answer 20

I didn't think it that way lol