int_{pi /4}^{pi /2} csc^2 x , dx = | vedclass

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(B) We need to evaluate the definite integral: $\int_{\pi /4}^{\pi /2} \csc^2 x \, dx$. Recall that the antiderivative of $\csc^2 x$ is $-\cot x$. App

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$1$

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(B) We need to evaluate the definite integral: $\int_{\pi /4}^{\pi /2} \csc^2 x \, dx$. Recall that the antiderivative of $\csc^2 x$ is $-\cot x$. Applying the Fundamental Theorem of Calculus: $\int_{\pi /4}^{\pi /2} \csc^2 x \, dx = [-\cot x]_{\pi /4}^{\pi /2}$ $= -(\cot(\frac{\pi}{2}) - \cot(\frac{\pi}{4}))$ Since $\cot(\frac{\pi}{2}) = 0$ and $\cot(\frac{\pi}{4}) = 1$: $= -(0 - 1) = 1$.

$\int_{\pi /4}^{\pi /2} \csc^2 x \, dx = $

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