Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves
x=0, y=1, x=y^4
about the line y=1

Question

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves
x=0, y=1, x=y^4
about the line y=1

b87lar · Answer

Express as function of x: $$x=y^4 \rightarrow y=x^{1/4}, x\geq 0 $$Rotating this function around y=1 we'll use the method of "washers." The radical function meets the line y=1 at x=1 so at each point 0<=x<=1, the radius of the washer is $$1-x^{1/4}$$Integrate over x: $$\pi \int_0^1 (1-x^{1/4})^2 dx = \pi/15$$Done!

anonymous · Answer

@b87lar thank you so much!!