Integration By Substitution With Examples plus Trig Sub
Today we are covering integration by substitution with examples plustrig substitution! This was the topic most voted by you so enjoy! Make sure to stick to the end to see how to deal with those tricky trig substitution integrals and how next week your topic could the next one!
What is integration by substitution and why do I need it?
Well integration by substitution allows us to transform integrals that look tricky or nasty into a much simpler and nicer form to deal with.
Example 1 with bounds 0:45
Example 2 when x doesn't cancel 3:57
Example 3 trig sub 6:08
So how do we integrate by substitution?
Well most integration by substitution examples follows the same process:
1. Find du/dx and make dx the subject.
2. Change any bounds using the u substitution.
3. Sub dx and u into the integral with new bounds and cancel any x terms you can.
4. If any x terms remain use original substitution to remove it.
5. Integrate
6. Sub bounds and you’re done!!
6.5 If there are no bounds to sub you sub back in for x using original substitution and add the plus C.
Let’s now look at some examples of how to integrate using substitution and how to integrate using trig substitution!
When integrating by substitution using trig substitution in order to integrate you will need to use trig identities. Also for the last step if there are no bounds you will need to draw a right angle triangle and use that to find the correct trig ratio in the answer.
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