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प्रश्न
Evaluate each of the following integral:
\[\int_0^\frac{\pi}{4} \sin2xdx\]
योग
उत्तर
\[\int_0^\frac{\pi}{4} \sin2xdx\]
\[ = \left.\frac{- \cos2x}{2}\right|_0^\frac{\pi}{4} \]
\[ = - \frac{1}{2}\left( \cos\frac{\pi}{2} - \cos0 \right)\]
\[ = - \frac{1}{2} \times \left( 0 - 1 \right)\]
\[ = \frac{1}{2}\]
\[ = \left.\frac{- \cos2x}{2}\right|_0^\frac{\pi}{4} \]
\[ = - \frac{1}{2}\left( \cos\frac{\pi}{2} - \cos0 \right)\]
\[ = - \frac{1}{2} \times \left( 0 - 1 \right)\]
\[ = \frac{1}{2}\]
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Definite Integrals
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