The region below the curve y = e^x + e^(-x) and the lines x = 0, x = ln4 is rotated 2π radians about the x-axis. Find the volume of the resulting solid.

We can use the formula for a Volume of Revolution: V =π ∫ (e^x + e^(-x))^2 dx, with limits x = 0, x = ln4.Expanding the brackets: (e^x + e^(-x))^2 = e^2x + 2 + e^(-2x).So: V = π ∫ (e^2x + 2 + e^(-2x)) dx = π [ (1/2)e^2x - (1/2)e^(-2x) + 2x ], evaluated with limits x = 0, x = ln4.Substituting in the limits we have:V = π( [(1/2)e^2ln4 - (1/2)e^(-2ln4) + 2ln4] - [(1/2) - (1/2) + 0] ) V = π [ (1/2)(4^2 - 4^(-2)) + 2ln4 ]Evaluating: V = π((255/32) + 2ln4).

RS
Answered by Rumen S. Maths tutor

3986 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

express x^2-4x+9 in the form (x-q)^2+y


How do I find the area under a curve between two points?


x = t^3 + t, y = t^2 +1, find dy/dx


Determine whether the line with equation 2x+ 3y + 4 = 0 is parallel to the line through the points with coordinates (9, 4) and (3, 8).


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning