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

Answer 1

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!

Answer 2

@b87lar thank you so much!!