Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
y=5x^2,y=x^2+3
2 answers
Cannot see sketches. Cannot copy and paste diagrams here.
integrate with respect to x, so you don't have horizontal strips that change boundary curves. Then, since the region is symmetric about x=0, the area is
2∫[0,√3/2] (x^2+3)-5x^2 dx
each vertical strip has a height equal to the distance between the curves.
2∫[0,√3/2] (x^2+3)-5x^2 dx
each vertical strip has a height equal to the distance between the curves.