The value of $\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\sin^{2} x}{1 + 2^{x}} d x i s :$

π/4

π/8

π/2

4π

Solution

π/4

$I = \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\sin^{2} x d x}{1 + 2^{x}} . . . (i) A l s o, I = \int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{2^{x} \sin^{2} x d x}{1 + 2^{x}} . . . . (i i) A d d i n g (i) a n d (i i) 2 I = \int_{- \frac{π}{2}}^{\frac{π}{2}} \sin^{2} x d x 2 I = 2 \int_{0}^{\frac{π}{2}} \sin^{2} x d x \Rightarrow I = \int_{0}^{\frac{π}{2}} \sin^{2} x d x . . . . (i i i) I = \int_{0}^{\frac{π}{2}} \cos^{2} x d x . . . . (i v) A d d i n g (i i i) a n d (i v) 2 I = \int_{0}^{\frac{π}{2}} d x = \frac{π}{2} \Rightarrow I = \frac{π}{4}$

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Integrals

The value of $\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\sin^{2} x}{1 + 2^{x}} d x i s :$

π/4

π/8

π/2

4π

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Mock Test Series

NCERT Sample Papers

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Integrals

The value of ∫-π2π2sin2x1+2xdx is: π/4 π/8 π/2 4π

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The value of $\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\sin^{2} x}{1 + 2^{x}} d x i s :$

π/4

π/8

π/2

4π