Question

find the coordinates of the point of integration of the curves y=x^2 and y^2=8x.sketch the two curves and find the area enclosed by the two.

Answer 1

http://www.wolframalpha.com/input/?i=plot+x^2,sqrt(8x)

That's the plot of both equations. Notice that y^2=8x is greater than y=x^2 between the two intersection points. To find the intersection points substitute the y=x^2 into the other equation. You should get x(x^3-8)=0

Finally the integral would be
\[\int\limits_{a}^{b} \sqrt(8x) - x^2 dx\]