Question

find the area bounded by the graph of the indicated equation over the given intervals
y= -x; y=0,
−2≤x≤1

Answer 1

Evaluate the integral
\[\int\limits_{-2}^{0}-xdx - \int\limits_{0}^{1}-xdx\]

Answer 2

It needs to be split into two integrals because from 0 to 1 the function is below the x-axis and thus the integral from 0 to 1 will be negative.
Since we are looking for area, we need to subtract the negative region (which will change the area to a positive value.)

Answer 3

thanks..this is what confuses me most as to which one subtracts which one?

Answer 4

0 - (-1/2* (-2)^2 - [-1/2* 1^2 - 0]

Answer 5

How about \[y= -x^2 + 10; y=0; -3\le x \le3\]

Answer 6

is this the same thing?