Finding the volume of a shaded region above a graph?
The diagram shows part of the curve y = x^2 + 1 . Find the volume obtained when the shaded region is rotated through 360° about the y -axis.
The shaded regions boundaries are the following: 0 <= x <= 2 and 1 <= y <= 5 .
Graph sketched here
The diagram shows part of the curve
The shaded regions boundaries are the following:
Graph sketched here
1 Answer
Sep 16, 2017
Explanation:
"for volume (V) rotated about the y-axis"
•color(white)(x)V=piint_c^d x^2dy
"here "c=1" and "d=5
y=x^2+1rArrx^2=y-1
rArrV=piint_1^5(y-1)dy
color(white)(rArrV)=pi[1/2y^2-y]_1^5
color(white)(rArrV)=pi[25/2-5-(1/2-1)]
color(white)(rArrV)=8pi" cubic units"
