Asked by TayB
Sketch the region enclosed by the given curves. Find its area.
y=7cos pi x, y=12x^2-3
y=7cos pi x, y=12x^2-3
Answers
Answered by
Steve
See
http://www.wolframalpha.com/input/?i=plot+y%3Dcos%28pi*x%29%2C+y%3D12x^2-3
the curves intersect at (-1/2,0) and (1/2,0).
So, it's just a straightforward integral. Since things are symmetric, the area is just
2∫[0,1/2] cos(πx)-(12x^2-3) dx
http://www.wolframalpha.com/input/?i=plot+y%3Dcos%28pi*x%29%2C+y%3D12x^2-3
the curves intersect at (-1/2,0) and (1/2,0).
So, it's just a straightforward integral. Since things are symmetric, the area is just
2∫[0,1/2] cos(πx)-(12x^2-3) dx