GATE Papers >> EEE >> 2017 >> Question No 17

Question No. 17 EEE | GATE 2017

Let $I=\;c\iint_R\;xy^2\;dxdy$, where R is the region shown in the figure and c = 6 × 10-4. The value of I equals _________. (Give the answer up to two decimal places.)


Answer : 0.99 to 1.01


Solution of Question No 17 of GATE 2017 EEE Paper

The equation of boundary of region R is y = 2x

I = c $\iint\limits_R$ xy2 dxdy = c $\int\limits_1^5\int\limits_0^{2x}$ xy2 dydx

I = c $\int\limits_1^5\times\left(\frac{y^3}3\right)_0^{2x}dx=c\int\limits_1^5\times\left(\frac{8x^3}3\right)dx=c\left[\frac{8x^5}{15}\right]_{1}^5$

I = 6 $\times$ 10-4 $\times\frac8{15}\times$ (55 - 15)

I = 0.99968

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