You need to find the volume of solid generated byrotating the triangle found between the function `f(x) = ax + b, x` axis and limits `x = 0` and `x = 1` , hence, you need to find first the equationof function f(x) whose graph passes through the points `(0,0)` ) and `(1,1)` such that:
`f(0) = 0 => 0 = b`
`f(1) = 1 => a*1 + b =1 => a = 1`
Substituting 1 for a and 0 for b in equation of the function f(x) yields `f(x) = x` .
Hence, you need to determine the volume generated rotating the triangle around x axis, such that:
`V = pi*int_0^1 f^2(x) dx => V = pi*int_0^1 x^2 dx`
`V = pi*x^3/3|_0^1`
Using the fundamental theorem of calculus yields:
`V = pi*(1^3/3 - 0^3/3) => V = pi/3`
Hence, evaluating the volume of solid generated by rotating the given triangle about x axis, yields `V = pi/3` .