Q. 52 - Calculus

Question

Consider the region between the graphs of $f\left(x\right)={\left(x-2\right)}^2$and $g\left(x\right)=x$ on $\left[1,4\right]$ For each line of rotation given in Exercises 51–54, 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 using appropriate method

For the region between the given graphs, use the disk, washer, or shell method depending on the axis of rotation.

Step 2: Evaluate

The volume is found by integrating the appropriate cross-sectional area formula over the given interval.