To evaluate the double integral \int ↙\stackrel{8}{0}⁡ (\int _{{\frac{y}{2}}}^{ (\frac{y}{2}) + 1}⁡ (\frac{2x−y}{2}) dx) dy we make the substitution u = (\frac{2x−y}{2}) and v = \frac{y}{2}. The integral will reduce to

Correct Answer is : ∫04⁡(∫01⁡2udu)dv

\int ↙\stackrel{4}{0}⁡ (\int ↙\stackrel{2}{0}⁡2\:u\:du) dv

\int ↙\stackrel{4}{0}⁡ (\int ↙\stackrel{1}{0}⁡2\:u\:du) dv

\int ↙\stackrel{4}{0}⁡ (\int ↙\stackrel{1}{0}\:u\:du) dv

\int ↙\stackrel{4}{0}⁡ (\int ↙\stackrel{2}{0}\:u\:du) dv

GATE Electrical Engineering (EE) 2014 Shift 2 Solved Paper

Question : 36 of 65

Marks: +1, -0

To evaluate the double integral

∫ ↙{0}↖{8}⁡ (∫ ↙{{\;{y}/{2}}}↖{ (\;{y}/{2}) + 1}⁡ (\;{2x−y}/{2}) dx) dy

we make the substitution

u = (\;{2x−y}/{2})

and

v = \;{y}/{2}

. The integral will reduce to

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