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

2963 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A particle of weight 15N is resting on a plane inclined at an angle of 30°. Find : a) the normal force exerted on the particle, b) the coefficient of friction between the particle and the plane, providing it is in limiting equilibrium


Show how '2sin(x)+sec(x+ π/6)=0' can be expressed as √3sin(x)cos(x)+cos^2(x)=0.


A curve has the equation 2x^2 + xy - y^2 +18 = 0. (1) Find the coordinates of the points where the tangent to the curve is parallel to the x-axis.


integrate xsin(x)


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences