Question

Sketch the region enclosed by x+y^2=20 and x+y=0. Decide whether to integrate with respect to x or y. Then find the area of the region.

Answer 1

the first equation is that of a parabola opening to the left. the other is a line. the region enclosed by these two graphs is better obtained by integrating with respect t y because the length of your representative rectangle is obtained by subtracting the right function - left function.

Answer 2

Integrate with respect to y

Answer 3

\[ \int\limits_{-4}^{5}(20-y^2)~dy-\int\limits_{-4}^{5}(-y)~dy\]

Answer 4

\[A=121\frac{1}{2}\]