∫ π 2 0 l o g ( t a n x + c o t x ) d x = Options: A . &nbspπ log 2 B . &nbsp−π log 2 C . &nbsp−π2 log 2 D . &nbspπ2 log 2

Answer: Option A : A ∫ π 2 0 l o g ( t a n x + c o t x ) d x = ∫ π 2 0 l o g [ 2 s i n 2 x ] d x = ∫ π 2 0 ( l o g 2 − l o g s i n 2 x ) d x = l o g 2 ( π 2 ) + ( π 2 ) l o g 2 = π l o g 2

∫π20 log(tan x+cot x)dx=

Question

\int_{0}^{\frac{π}{2}} l o g (t a n x + c o t x) d x =

Options:

A . π log 2

B . −π log 2

C . −π2 log 2

D . π2 log 2

Answer: Option A
:
A

\int_{0}^{\frac{π}{2}} l o g (t a n x + c o t x) d x = \int_{0}^{\frac{π}{2}} l o g [\frac{2}{s i n 2 x}] d x

= \int_{0}^{\frac{π}{2}} (l o g 2 - l o g s i n 2 x) d x = l o g 2 (\frac{π}{2}) + (\frac{π}{2}) l o g 2 = π l o g 2

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