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Numerade Educator

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Problem 74 Hard Difficulty

Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd function and use that fact to show that
$$ 0 \le \int^3_{-2} \sin \sqrt[3]{x} \, dx \le 1 $$

Answer

$\int_{a}^{b} f_{1}(x) d x \leq \int_{a}^{b} f(x) d x \leq \int_{a}^{b} f_{2}(x) d x$

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Video Transcript

we know that we can use the metric functions as a shortcut to figure out the integral. Which means we can see if we can prove if this function is odd or even. Okay. What this means is that where we have positive acts, we're now gonna plug in negative acts, and then we're gonna simplify. As you can see, we can see we end up with negative aftereffects, Which means that half of axe is indeed an odd function. Therefore, we know there's a property that from negative, eh? Awful vax D X is equivalent to zero. Therefore, we know that without even doing any mathematical calculations, we know the solution to this is going to be zero, and this is the proof that we can drive.