Question

Calculus question! Need help ASAP!!

Let R be the region in the first quadrant that is enclosed by the graph of y=4-x^2, y=3x and the y-axis.

a. Find the exact area of r.
b. Find the volume of the solid obtained by revolving R about the x-axis.
c. Find the volume of the solid obtained by revolving R about the y-axis.
d. Set up but do not evaluate the definite integral whose value is the volume of the solid. Obtained by revolving R about the line y=-2.

Answer 1

@sourwing help me out here please

Answer 2

At what point did you need help? From the start?
I recommend having a graph of the curves creating the region.

Answer 3

I'm not try to get only answers here. But I need to know how to do all of it.

Answer 4

That is fine.
The graph of the situation shows you some useful information. If you can visually see the region, you can get a better grasp on where things are intersecting and placed with respect to one another.

The reason it is important is primarily to make setting up the integrals more convenient. In general, the area under a curve is given by its definite integral over a domain. The area between two graphs is the difference in their areas, with the larger function is subtracting the smaller function.

Answer 5

I'm listening

Answer 6

Sorry, y-axis and not x-axis. The region is nudging up against the y-axis going vertically.