Integration using Trig identities
The goal is to convert the multiplication of terms to be addition of simple terms.
▶ Cheatsheet on previous note: Basic Integral Rules
▶ Cheatsheet on previous note:Basic Differential Rules
▶ Cheatsheet on previous note: All trig identities
▶ Back to previous note on: U-substitution → Chain Rule
Refer to Khan academy: Integrating using trigonometric identities
Example
We can identify there's a
Integral trig rule
we can apply on this problem:Therefore we're gonna organize it a bit with
u-substitution
and get the answer:
Example
This integrand has an odd power of
sin(x)
, so we're gonna leavesin(x)
alone and make an even power forsin(x)
, then makeu-substitution
upon it:And also we need to change the boundaries for the integral:
Now we can start to integrate:
Example
We're gonna use a
trig-integral-rule
and atrig identity
:Then apply them:
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