engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Calculus Multiple Integrals
A definite double integral is given below, then, evaluation of the double integral over the region R will be __
\(I = \;\mathop \smallint \nolimits_{x\; = \;0}^{x\; = \;r} \mathop \smallint \nolimits_{y\; = \;0}^{\sqrt {{r^2} - {x^2}} } \left( {y{r^2}} \right)\;dx.dy\)
Where R is the region on X - Y plane for the function given as, \(y = \sqrt {{r^2} - {x^2}} \) and r ∈ [0, 5]Enter numerical value using the virtual keypad. Round off where necessary.