Need reduction formula for this.. Plz help
- Thread starter mrgthiru
- Start date
You really should look it up yourself. I'm sure most of us don't have these integrals memorised.
Your integral is: \(\displaystyle \L\ \int sin^{-m}(x)cos^{-n}(x)\ dx\).
You might want to use the fact that if y is the integrand:
\(\displaystyle \L\ \frac{dy}{dx}\ = ncos^{1-n}sin^{1-m}(x) - msin^{-m - 1}(x)cos^{1 - n}(x)\)
\(\displaystyle \L\ = ncos(x)cos^{-n}(x)sin(x)sin^{-m}(x) - msin^{-m}(x)cot(x)cos^{-n}(x)\)
\(\displaystyle \L\ = nycos(x)sin(x) - mycot(x)\)
I'm sure there's some concrete formula out there devised by someone clever that splits the integral using integration by parts, which is why I reinforce you find one yourself.
Your integral is: \(\displaystyle \L\ \int sin^{-m}(x)cos^{-n}(x)\ dx\).
You might want to use the fact that if y is the integrand:
\(\displaystyle \L\ \frac{dy}{dx}\ = ncos^{1-n}sin^{1-m}(x) - msin^{-m - 1}(x)cos^{1 - n}(x)\)
\(\displaystyle \L\ = ncos(x)cos^{-n}(x)sin(x)sin^{-m}(x) - msin^{-m}(x)cot(x)cos^{-n}(x)\)
\(\displaystyle \L\ = nycos(x)sin(x) - mycot(x)\)
I'm sure there's some concrete formula out there devised by someone clever that splits the integral using integration by parts, which is why I reinforce you find one yourself.
