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Problem 24

Determine a region whose area is equal to the giv…

01:05
Problem 23

Use Definition 2 to find an expression for the area under the graph of $ f $ as a limit. Do not evaluate the limit.

$ f(x) = \sqrt{\sin x}, \hspace{5mm} 0 \le x \le \pi $

Answer

$\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \sqrt{\sin \left(\frac{\pi i}{n}\right)} \cdot \frac{\pi}{n}$



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Video Transcript

to solve this problem, we must first calculate Delta acts, which is pi minus zero. Divide by on which gives us pi over end and simplest form, which means now we can plug in the formula. We know we have exit by which is pi I over and and Delta X purity establishes pi over an which means we have the limit is un approaches Infinity square of sign of this value over here, Axl by times pi over end which is our delta X.

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