Integration doubt ....

plzzz integrate this ∫11+5cosx from 0 to Î

4 Answers

29
govind ·

use the property a∫b f(x) = a∫b f(a+b-x)

I = \int_{0}^{\pi }{\frac{dx}{1+5^{cosx}}} = \int_{0}^{\pi }{\frac{dx}{1+5^{-cosx}}}

2I = \int_{0}^{\pi }dx \Rightarrow I = \frac{\pi }{2}

39
Pritish Chakraborty ·

Since f(x) = f(-x), this is an even function.

\int_{0}^{\pi }{\frac{1}{1+5^{cosx}}} = 2\int_{0}^{\frac{\pi}{2} }{\frac{1}{1+5^{cosx}}}

2\int_{0}^{\frac{\pi}{2} }{\frac{1}{1+5^{cosx}}} = 2\int_{0}^{\frac{\pi}{2} }{\frac{1}{1+5^{cos(\frac{\pi}{2} - x)}}} = 2\int_{0}^{\frac{\pi}{2} }{\frac{1}{1+5^{sinx}}}

Does this make a difference? lola
haha..govind got it :P

1
Manmay kumar Mohanty ·

no pritish i thnk it's to approach solution by ur method.
Applying govind's method is the way i wuld have gone for .....

1
utd4ever ·

hey thanx that was easy actually i did the same thing but screwed up the adittion LOL ...

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