Find the volume of the solid of revolution formed by revolvi

Find the volume of the solid of revolution formed by revolving the region bounded by f(x)-3x2 and g(x) = 5X + 2 about the x-axis

First you need to find the oints of intersection:

3x^2 = 5x+2

3x^2 - 5x - 2 = 0

(3x+1)(x-2) = 0

So the points of intersection is: x = -1/3 , 2

So the volume is:

V = * int (5x+2)² - (3x²)² dx (x from -1/3 to 2) =

((5x+2)³/15 - 9/5 x⁵) (-1/3 < x < 2) =

((5*2+2)³/15 - 9/5 * 2⁵) - ((5/3+2)³/15 - 9/5 * (5/3)⁵) =

31372/405

243.353