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The value of \(\int^2_0\int^x_0y\ dy\ dx\)1. \(\frac{2}{3}\)2. 13. \(\frac{4}{3}\)4. \(\frac{3}{4}\) |
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Answer» Correct Answer - Option 3 : \(\frac{4}{3}\) Explanation: \(f(x)=\int^2_0\int^x_0y\ dydx\) \(f(x)= \mathop \smallint \limits_0^2 \left[ { \frac{{{y^2}}}{2}} \right]_0^{{x}}dx\) \(f(x)=\int^2_0[\frac{x^2}{2}-0]\ dx\) \(f(x)=\frac{1}{2}\int^2_0{x^2}\ dx\) \(f(x)= \frac{1}{2} \left[ { \frac{{{x^3}}}{3}} \right]_0^{{2}}\) \(f(x)=\frac{1}{2}(\frac{2^3}{3}-0)\) \(f(x) = \frac{4}{3}\) |
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