I don't think I can do it 6

Calculus Level 2

Find the volume of the body bounded by the surfaces y = 1 + x 2 , z = 3 x , y = 5 , z = 0 y=1+x^2,z=3x,y=5,z=0 and located in the first octant.

If the volume is x x cu. units. Find x x .


The answer is 12.

Akshat Sharda by Akshat Sharda , 21, India

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1 solution

Otto Bretscher
Dec 6, 2015

This is the volume under the graph of f ( x , y ) = 3 x f(x,y)=3x above the region given by 0 ≤ x ≤ 2 0\leq x \leq 2 and 1 + x 2 ≤ y ≤ 5 1+x^2\leq y \leq 5 :

∫ 0 2 ∫ 1 + x 2 5 3 x d y d x = ∫ 0 2 3 x ( 4 − x 2 ) d x = 12 \int_{0}^{2}\int_{1+x^2}^{5}3xdydx=\int_{0}^{2}3x(4-x^2)dx=12

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