The value of the definite integral int_{0}^{p | vedclass

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(D) To evaluate the integral $I = \int_{0}^{\pi/4} \sin(2x) \, dx$,we use the standard integration formula $\int \sin(ax) \, dx = -\frac{\cos(ax)}{a}

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$1/2$

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(D) To evaluate the integral $I = \int_{0}^{\pi/4} \sin(2x) \, dx$,we use the standard integration formula $\int \sin(ax) \, dx = -\frac{\cos(ax)}{a} + C$.Applying this to the given definite integral:$I = \left[ -\frac{\cos(2x)}{2} \right]_{0}^{\pi/4}$Substitute the upper and lower limits:$I = -\frac{1}{2} \left[ \cos(2 \cdot \frac{\pi}{4}) - \cos(2 \cdot 0) \right]$$I = -\frac{1}{2} \left[ \cos(\frac{\pi}{2}) - \cos(0) \right]$Since $\cos(\frac{\pi}{2}) = 0$ and $\cos(0) = 1$:$I = -\frac{1}{2} [0 - 1]$$I = -\frac{1}{2} [-1] = \frac{1}{2}$.

The value of the definite integral $\int_{0}^{\pi/4} \sin(2x) \, dx$ is:

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