Explain how integration via substitution works.

The function in terms of x should be broken down into two easier to integrate functions, like so f(x) = g(h(x)). if we say that u=h(x) is our substitution then we can integrate in terms of u now, however the dx term must also be written in terms of u. for this, differentiate u with respect to x using the function h(x) giving du/dx. now du and dx can be split up and dx can be substituted into the integral in terms of u and du. This can also be done with boundary conditions at the top and bottom of the sigma but it is not necessary as they can be put in when u is converted back in terms of x after the integration.
now the integral with respect to u can be performed. once this is done x can be substituted back in using the relation u=h(x). (this explanation would be aided with a step by step example).

DF
Answered by Daniel F. Maths tutor

2842 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Why does integration by parts work?


Differentiate with respect to x and write in its simpliest form, Y=(2x-3)/x^2?


Solve e^x-6e^-x=1


Given that the increase in the volume of a cube is given by dV/dt = t^3 + 5 (cm^3/s). The volume of the cube is initially at 5 cm^3. Find the volume of the cube at time t = 4.


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