Find the area of a region bounded by the curves y = 10 - x -2x^2 and y = 7x.

I got to the point of taking the antiderivative but whenever I try to solve my integral I end up with a negative area which I know isn't correct

Question

Find the area of a region bounded by the curves y = 10 - x -2x^2 and y = 7x.

I got to the point of taking the antiderivative but whenever I try to solve my integral I end up with a negative area which I know isn't correct

kainui · Answer

Perhaps you're subtracting them backwards? The integral you think is larger might really be smaller, so when you're subtracting your area you get a negative number. Just flop the sign around if that's the case.

kainui · Answer

|dw:1335407112042:dw| Actually from this picture, you can see that it does go into the negative area, so it is possible to have a negative area. The question is too vague for me to answer though. Do you want the absolute volume or net volume? Is it bounded by the x-axis? You can change your bounds of integration and integrate parts of it to only find the area of the absolute space and use a little bit of geometrical thinking to work it out.