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Let \(f:[0,\frac{\pi}{2}]→[0,1]\) be the function defined by \(f(x)=\sin^2x\) and let \(g:[0,\frac{\pi}{2}]→[0,\infin)\) be the function defined by \(g(x)=\sqrt{\frac{\pi x}{2}=x^2}\).
Question: 1
The value of \(\int\limits_{0}^{\frac{\pi}{2}}f(x)g(x)dx-\int\limits_{0}^{\frac{\pi}{2}}g(x)dx\) is ______.
The value of \(\int\limits_{0}^{\frac{\pi}{2}}f(x)g(x)dx-\int\limits_{0}^{\frac{\pi}{2}}g(x)dx\) is ______.
Updated On: Jun 20, 2024
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Correct Answer: 0
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The correct answer is: 0.
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Question: 2
The value of \(\frac{16}{\pi^3}\int\limits_{0}^{\frac{\pi}{2}}f(x)g(x)dx\) is __________.
The value of \(\frac{16}{\pi^3}\int\limits_{0}^{\frac{\pi}{2}}f(x)g(x)dx\) is __________.
Updated On: Jun 20, 2024
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Correct Answer: 0.25
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The correct answer is: 0.25.
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