Integration by substitution, sometimes called changing the variable, is used when an integral cannot be integrated by standard means. The method involves changing the variable to make the integral into one that is easily recognisable and can be then integrated.

You may want to try the questions first as part of your maths revision before looking at the video tutorial and worked solutions.

Worked solution to (1)

Worked solution to (2)

Some integrals contain square roots. In these you can have two types of substitution. Make sure you know how to handle these types.

Worked solution to (3a)

Worked solution to (3b)

 

Then you can have integrals of trig functions

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and exponential functions

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Some integrals have limits (definite integrals). Make sure you know how to set these out, change limits and work efficiently through the problem.

Worked solution to (6)

the limits in question 7 are from 0 to pie / 6

Worked solution to (7)

 

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