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)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)

Answered by Stephen B. Maths tutor

4871 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A projectile is thrown from the ground at 30 degrees from the horizontal direction with an initial speed of 20m/s. What is the horizontal distance travelled before it hits the ground? Take the acceleration due to gravity as 9.8m/s^2


For sketching the graph of the modulus of f(x) (in graph transformations), why do we reflect in the x-axis anything that is below it?


Given that x = 1/2 is a root of the equation 2x^3 – 9x^2 + kx – 13 = 0, find the value of k and the other roots of the equation.


Show that cosec(2x) + cot(2x) = cot(x)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences