V = π Plug the function being rotated into the formula Simplify
V = π(2x 2 )| V = π [2(1 2 )- 2(0 2 )] V = 2π Integrate the simplified solution Solve using the given interval
When you have two functions and you have to find the area of a region bounded by the two functions revolved around the x-axis use the formula: V = π
Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x 3 and line y = x around the x-axis.
x = x 3 at x = 0, 1 x is the outer function and x 3 is the inner function Determine the interval by finding where the two functions intersect Then determine which is the inner and outer radiuses by looking at the graph
V = π V = π(x 3 /3 – x 7 /7)| V = π[(1/3)-(1/7)] V = 4π/21 Plug in the values into the formula Simplify the integral Integrate Solve
Always put dx at the end of your integrals Dont forget the π!!!!! Square before subtracting when using the washer method Solids of revolution have been a FRQ topic for the past 6 years