2 quick easy q's (1 Viewer)

[Chris_S]

How do i -
1- Integrate 2sin ^2 x
2- Integrate cos ^2 x

Thank you

 

[InteGrand]

Use these identities to convert the squares:

 

[Flop21]

Use these identities to convert the squares:

What if the power is not 2, but higher, e.g. 3 or 4?

 

[VBN2470]

What if the power is not 2, but higher, e.g. 3 or 4?

You would have to manipulate the expression so that it becomes a suitable integrand. For example

which is simple to integrate using the substitution

But for something like , you would need to express it as and rearrange furthermore the simplify.

There is a general (recursive) formula to integrate sine and cosine functions of higher powers, and the integral will depend on whether the powers are odd or even numbers. (Mainly req'd for 4U students)

http://www.sosmath.com/calculus/integration/powerproduct/powerproduct.html

 

[InteGrand]

Speaking of integral formulas, there is a plethora of them here: https://en.wikipedia.org/wiki/Lists_of_integrals#Lists_of_integrals

(Take a look at the one for rational functions!: https://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions )