₀^{π/2}²x\,dx - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.9
Evaluate the definite integrals in Exercises 176 to 195.

Question : 187 of 271

Marks: +1, -0

\int\limits_{0}^{\pi/2}\cos^2x\,dx

Solution:

\int\limits_{0}^{\pi/2}\cos^2x\,dx

=\int\limits_{0}^{\pi/2}\frac{1+\cos2x}{2}\,dx

=\left[\frac{1}{2}\left(x+\frac{\sin2x}{2}\right)\right]_{0}^{\pi/2}

=\frac{1}{2}\left[\left(\frac{\pi}{2}-0\right)+\left(\frac{\sin\pi}{2}-\frac{\sin0}{2}\right)\right]

=\frac{\pi}{4}

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