_{-π/2}^{π/2} ² x dx - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.11
By using the properties of definite integrals, evaluate the integrals in Exercises 208 to 225.

Question : 217 of 271

Marks: +1, -0

\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^2 x dx

Solution:

Let

I=\int\limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^2 x dx

I=2\int\limits_{0}^{\frac{\pi}{2}} \sin^2 x dx

[

\because \sin^2 x

is an even function]

=2\int\limits_{0}^{\frac{\pi}{2}} \left( \frac{1-\cos 2x}{2} \right) dx

=\left[ x - \frac{\sin 2x}{0} \right]_{0}^{\frac{\pi}{2}}

\Rightarrow I = \frac{\pi}{2}

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