Q. 50 - Calculus

Question

Consider the region between the graphs of $f\left(x\right)=x^2$ and $g\left(x\right)=2x$ on [0, 2]. For each line of rotation given in Exercises 47–50, use definite integrals to find the volume of the resulting solid.

Step-by-Step Solution

Answer

The volume of the solid is

Step 1: Set up the integral

For the region between \( f(x) = x^2 \) and \( g(x) = 2x \) on \( [0, 2] \), use the appropriate method (washer or shell) based on the line of rotation.

Step 2: Evaluate

Compute the definite integral to find the volume of the resulting solid of revolution.