Question

Find the area between the two curves

y=x^4-10x^2+36 and y=3x^2

Answer 1

what's the trouble? You are adding up a bunch of thin rectangles, with width dx and height the distance between the curves. The curves intersect at (±2,12) and (±3,27). Since both functions are even, we can use symmetry and use

a = 2∫[2,3] (3x^2)-(x^4-10x^2+36) dx = 124/15

Answer 2

@Steve, my teacher says the answer is supposed to be 1436/15 but I have to figure out how I got it.

Find the area of the regions that are enclosed by the curves.

Answer 3

surely you can do the math.

∫[2,3] (3x^2)-(x^4-10x^2+36) dx
= ∫[2,3] -x^4 + 13x^2 - 36 dx
= -x^5/5 + 13/3 x^3 - 36x [2,3]
= (-243/5 + 13*27/3 - 36*3)-(-32/5 + 13/3 * 8 - 36*2)
= 62/15

double that for 124/15

Now you need to ask your teacher how 1436/15 can be right. Just looking at the graphs, you can see that the area is very small. 1436/15 is almost 100!

http://www.wolframalpha.com/input/?i=x^4-10x^2%2B36+%3D+3x^2