Transcript:

Hi, my name is Stefan. Today, I'm going to be speaking on how to integrate using trig substitutions. Let's say for example we have the integral of X cubed/ the square root of 16 - X squared. There's a trig substitution that says if you have the square root of A squared - X squared that you let X = A sine theta. Now in substituting this in we get the integral of 4 sine theta cubed/the square root of 16 which is 4 squared - 4 sine theta quantity squared and our DX is 4 cosine theta, D theta. Now, this is good because if you look at our denominator you see a 1 - sine squared which of course = cosine squared and this allows us to simplify and then in our answer we get 4 squared times 16 - X squared + 16 - X squared quantity cubed + C/3. And that's how you integrate using trig substitutions.