Evaluate the definite integral int_{0}^{frac{ | vedclass

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(A) Let $I = \int_{0}^{\frac{\pi}{4}} \sin 2x \,dx$. The antiderivative of $\sin 2x$ is $\int \sin 2x \,dx = -\frac{\cos 2x}{2}$. By the Second Fundam

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$1/2$

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(A) Let $I = \int_{0}^{\frac{\pi}{4}} \sin 2x \,dx$. The antiderivative of $\sin 2x$ is $\int \sin 2x \,dx = -\frac{\cos 2x}{2}$. By the Second Fundamental Theorem of Calculus,we have: $I = \left[ -\frac{\cos 2x}{2} \right]_{0}^{\frac{\pi}{4}}$ $I = -\frac{1}{2} \left[ \cos 2\left(\frac{\pi}{4}\right) - \cos 2(0) \right]$ $I = -\frac{1}{2} \left[ \cos\left(\frac{\pi}{2}\right) - \cos(0) \right]$ Since $\cos(\frac{\pi}{2}) = 0$ and $\cos(0) = 1$,we get: $I = -\frac{1}{2} [0 - 1] = \frac{1}{2}$.

Evaluate the definite integral $\int_{0}^{\frac{\pi}{4}} \sin 2x \,dx$.

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