The problem of definite integral is to find the volume of the figure surrounded by y = x ^ 2 and y = 10 rotating around the Y axis,
The intersection coordinates of y = x ^ 2 and y = 10 are (- √ 10,10), and (√ 10,10),
Take Y axis as symmetry axis, left and right symmetry,
x=±√y,
V=∫(0→10)π(√y)^2dy
=∫(0→10)πydy
=πy^2/2(0→10)
=π(10^2-0)/2=50π.
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