Hello,

We're currently doing integration on areas between two or more functions, and i'm having trouble with it.

These are the instructions for most of the questions in the homework:

"Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Find the area of the region."

I was wondering if you could explain the general procedure behind this? Here are two of the problems I attempted, but which I don't think are correct.

1) y = sinx, y = x, x = pi/2, x = pi

I did: integral from pi/2 to pi of: (x - sinx)dx

= (1/2)*x^2 + cosx | pi/2 to pi

= [pi^2/2 - 1] - [pi^2/8 + 0] = -pi^2/2 - 1 = -5.9348.

Negative? I didn't think that could be right. I'm also kind of confused about which of those functions is considered to be the 'top' function, since the area between the function is the integral of f(x)-g(x). On the graph it looks like they touch each other.

2) x = y^2 - 4y, x = 2y - y^2. from y = 0 to y = 3

I did: integral from 0 to 3 of (y^2 - 4y - 2y + y^2)dy

= integral from 0 to 3 of (2y^2 - 6y)dy

= (2/3)*y^3 - 3y^2 | 0 to 3

= [18 - 27] - [0 - 0] = -9? Another negative

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