Let R denote the region bounded by the curve y=x^3 and the lines x=0 and x=4. Find the volume generated when R is rotated 360 degrees about the x axis.
The area of a circle is given by (pi)r2 and the area generated by R can be considered as an infinite number of circular areas.
Thus, we can write the area generated by R as the integral of (pi)(x3)2 between x=0 and x=4.
The (indefinate) integral is: (pi)6x5
so the area is: (pi)6(45-05)=(pi)6(1024-0)
=6144(pi)
SB
Related Maths A Level answers
All answers ▸Express 4 sin(x) – 8 cos(x) in the form R sin(x-a), where R and a are constants, R >0 and 0< a< π/2
Find the equation of the tangent to the curve y = (2x -3)^3 at the point (1, - 1), giving your answer in the form y = mx + c.
(i) Prove sin(θ)/cos(θ) + cos(θ)/sin(θ) = 2cosec(2θ) , (ii) draw draph of y = 2cosec(2θ) for 0<θ< 360°, (iii) solve to 1 d.p. : sin(θ)/cos(θ) + cos(θ)/sin(θ) = 3.
What is the differential of (14x^3-3x^2)^3