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Evaluate $\int\limits_0^1\int\limits_0^x xy\space dydx$

written 9.5 years ago by teamques10 ★ 70k

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engineering mathematics

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written 9.5 years ago by teamques10 ★ 70k

Integrating w.r.t. y

$$I= \int\limits^1_{x=0} x\int\limits^x_{y=0}y\space dydx$$

$=\int\limits^1_{x=0}x\Bigg[\dfrac {y^2}2\Bigg]^x_0 dx \\ =\int\limits^1_{x=0}x\Bigg[\dfrac {x^2}2\Bigg] dx \\ =\int\limits^1_{0}\Bigg[\dfrac {x^3}2\Bigg]dx \\ =\dfrac 12\Bigg[\dfrac {x^2}4\Bigg]^1_0 \\ =\dfrac 18$

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