Calculus
posted by Mark .
Let R be the region bounded by y=−3(x−1)(x−3) and the xaxis. Let S be the solid obtained by rotating R about the yaxis. The volume of S is given by Nπ. What is the value of N?

v = ∫[1,3] 2πrh dx
where r = x and h = y = −3(x−1)(x−3) so
v = ∫[1,3] 2πx(−3(x−1)(x−3)) dx
= 6π ∫[1,3] x^3  4x^2 + 3x dx
= 16π
Respond to this Question
Similar Questions

Calculus
A solid is formed by rotating the region bounded by the curve y=e−3x2 and the xaxis between x=0 and x=1, around the xaxis. The volume of this solid is 3(1−e−3). Assuming the solid has constant density , find x and … 
Calculus
solid is formed by rotating the region bounded by the curve y=e−3x^2 and the xaxis between x=0 and x=1, around the xaxis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and … 
Calculus
solid is formed by rotating the region bounded by the curve y=e−3x^2 and the xaxis between x=0 and x=1, around the xaxis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and … 
Math
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = (64 − x^2)^(1/4), y = 0, x = 6, x = 7; about the xaxis 
math calculus
The volume of the solid obtained by rotating the region bounded by y=x^2−2x and y=x about the line y=9, has the form a/bπ, where a and b are positive coprime integers. What is the value of a+b? 
calculus
he volume of the solid obtained by rotating the region bounded by x=(y−2)^2 and y=x about the xaxis has the form N/2π. What is the value of N? 
calculus help
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − 1/2x, y = 0, x = 0, x = 1; about the xaxis V = ? 
calculus
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y=4,x=5−(y−1) 2 ; 
Ap calc
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the xaxis. x + y = 3, x = 4 − (y − 1)^2 
Cal
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^2, y=0, x=4, x=5; about y=−2