Peruvian marinera

Calculus Level 4

Let there be a region R:{(x,y)  x1/4+y41}R:\{(x,y) \ | \ x^{1/4}+y^{4} \leq 1\}. What is the volume of the solid generated when RR is rotated around the line x=0?x=0? Give your answer to 3 decimal places.


Note: You may use a calculator for the final step of your calculation.

This question was posed by my calculus teacher as the last and higher value exercise on the third Calculus I test.
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