A -0- -sin 2 x -1- a x dx -A- -B- -2C- a -2D- a-

The correct option is B π/2 I= ∫_ π^πsin^2x/1+a^xdx I=∫_ π^πa^xsin^2x/1+a^xdx 2I=∫_ π^πsin^2xdx=π I=π/2 ...

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Definite Integral as Limit of Sum

a >0, ∫-ππsin...

Question

$a > 0, π \int - π \frac{s i n^{2} x}{1 + a^{x}} d x =$

$\frac{π}{2}$

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$π$

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$\frac{a π}{2}$

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$a π$

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Solution

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If in a $△ A B C, a^{2} c o s^{2} A = b^{2} + c^{2}$ then

a>0, $\int_{- π}^{π} \frac{s i n^{2} x}{1 + a^{x}} d x =$

a > 0

\int_{- π}^{π} \frac{{sin}^{2} x}{1 + a^{x}} d x

I = \int_{- π}^{π} \frac{{sin}^{2} x}{1 + a^{x}} d x

a > 0,

I

f (x) = {sin}^{- 1} [x^{2} + \frac{1}{2}] + {cos}^{- 1} [x^{2} - \frac{1}{2}]

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