Finding Geometric area bounded by y= sinx and y = cosx

Find the geometric area bounded by y = sinx and y = cosx between the first two positive values of x at which these curves intersect.

I see more than one intersection. Am I going about this the wrong way?

Hello

Anon E is right

I just want to add some explanations

Here is the figure. The requested area is between A and B

http://img3.imageshack.us/img3/9307/inte…

A primitive of (sinx - cosx) is (-sinx - cosx)

From π/4 to 5π/4

It gives

(- sin 5π/4 - cos 5π/4) - ( - sin π/4 - cos π/4) = - (-√2/2) - (-√2/2) + (√2/2) + (√2/2) = 4(√2/2) = 2√2

Hope it helped

Bye !

Intersection points can be found by setting the functions equal to each other:
sinx = cosx
tanx = 1
x = arctan(1)
x = π/4 + nπ (tan is periodic over π)

Therefore, the first 2 positive intersection points occur at x = π/4, 5π/4.
In this region, sinx is on top of cosx, so the function you need to integrate is [sinx - cosx] over the interval above.

Ans. = 2√2