Question

the base of a solid is bounded by y = √ x , y = 0 , x = 2 , and x = 6 . its cross-sections, taken perpendicular to the x-axis, are squares. find the volume of the solid in cubic units. show all work.

Answer 1

16 cubic units

Explanation:

`\displaystyle V=\int^b_aA(x)\,dx\\\\V=\int^6_2(√(x))^2\,dx\\\\V=\int^6_2x\,dx\\\\V=(1)/(2)x^2\biggr|^6_2\\\\V=(1)/(2)(6)^2-(1)/(2)(2)^2\\\\V=(1)/(2)(36)-(1)/(2)(4)\\\\V=18-2\\\\V=16`

A(x) represents the area of the cross-section, so in this case, we square
`√(x)-0` which is just
`√(x)`