The region R is bounded by the curve y=sqrt(x)+5/sqrt(x) the x-axis and the lines x = 3, x = 4. Find the volume generated when R is rotated through four right-angles about the x-axis. Give your answer correct to the nearest integer.

The general formula for a volume of rotation is pi times the integral of y^2. The first step is to square y. this can be done by squaring the first term, squaring the last term and finding twice the product. Add all these answers together. Now integrate this firstly as an infinite intergration to get x+25/x+10. Now impose the limits and multiply by pi to give 65 units cubed.

Answered by Matthew H. Maths tutor

5954 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The line y=5-x intersects the curve y=x^2-3x+2 at the points P and Q. Find the (x,y) coordinates of P and Q.


Solve the differential equation dx/dt=-6*x , given when t=0 x=7.


Differentiate sin(2x)/x^2 w.r.t. x


The gradient of the curve at point (x,y) is given by dy/dx = [7 sqrt(x^5)] -4. where x>0. Find the equation of the curve given that the curve passes through the point 1,3.


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