A rough sketch and some quick easy algebra shows that the curve intersects the lines at (2,2) and (14,4)
and the two straight lines intersect at (4,4)
so in 2 parts ....
V = π∫( x^2 - (x+2) ) dx from 2 to 4 + π∫(16 - (x+2))dx from 4 to 14
= π [(1/3)x^3 - (1/2)x^2 - 2x] from 2 to 4 + π[ 16x - (1/2)x^2 - 2x] from 4 to 14
I will let you do the arithmetic
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis:
Y=sqrt(x+2), y=x,y=4
1 answer
1 answer