Question

Calc: Find the area of the region between the curves y=sin(pix/2) and y=x (picture)

Answer 1

as you can see in the pic, there are two regions that we'd need to calculate to get the total area between these curves, but I think it'd be easier to find the area of one and then double it

Answer 2

so lets find the area of the region in the first quadrant. it looks like they intersect at 0 and 1 so those will be out limits of integration.

Answer 3

our*

Answer 4

the sine function is on top of y = x so we'll find the area of the top function and then subtract the bottom one to find the area between

Answer 5

for point of intersection how did you get 1? did you get them equal to each other? if we did not have an exact graph to look at

Answer 6

so we integrate:
\[\int\limits_{0}^{1}(\sin(\frac{ \pi x }{2}) - x)dx\]

Answer 7

yes

Answer 8

ok let me try that real quick and see what i get

Answer 9

- cos pi -1/4

Answer 10

-cos(pi/4)-1/2

Answer 11

I'm getting a different answer, can you show me how you integrated?