Definite Integral Problem: Sketch the region by x+y^2=30 and x+y=0. Decide whether to integrate with respect?

Question

to x or y, then find the area of the region.

i have no idea how to even start this problem if you could explain thatd be great! thanks!

Answer 1

Surely you can plot the equations that define the region. In fact, I find that, for me, a graph is necessary in order to make informed decisions about how to proceed. The plot looks like this:

http://i20.tinypic.com/334m2z8.gif

Integration with respect to x is doable, but you would need two integrals since for some x, the lower boundary is the line, and for other x the lower boundary is the lower half of the parabola. This difficulty doesn't arise with y-integration; (right boundary - left boundary) is always (parabola - line).

So the integrand is (30 - y²) -(-y), or 30 - y² + y

The limits are the y-values of the two intersection points between the parabola and the line; that is, where 30 - y² = -y. I'll let you find those.

I get an answer just under 222.

Answer 2

square root of 56 = 7.48 (2dp) so x + y = 7.48