Which statement best explains why the volume integral must be written as the sum of…
MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Which statement best explains why the volume integral must be written as the sum of more than one definite integral when the region bounded by y=x3 and y=3x for 0≤x≤3 is revolved about the x-axis?
(a) Because the curves intersect inside the interval, each one lies farther from the x-axis on a different subinterval, so the washer set-up must be split into two definite integrals.
(b) Because y=3x is farther from the x-axis than y=x3 over the entire interval, a second integral is required only to subtract the hollow region carved out by y=x3.
(c) Because both curves cross the x-axis at x=0, part of the region is above the axis and part is below it, forcing separate integrals for the two portions.
(d) Because using a single integral would count the volume near the point of intersection twice, splitting the integral prevents that double counting.