Question

Question 2 6 Evaluate the integral TV ELM Vx2 + y2 dydx 2

Please be fast,, I have just 30 mins left.

Answer 1

We have to evaluate the integral I ir I Svezy dydx TE ។ het ✓8-y² first evaluate Je?y dy dx . 3 Before that let us Sketch the figures So x=y straight an angle 45° with the x-anis. Here x= ✓ 8- y² » x = 8-92. c) * +y? 8 which is with origin as center and radius ava. us plot (limits given in integral). passing through origin which makes line a circle it ały?:8 i 122 we move So Lif the dotted line L from _ Yoo to y = 2, we will get the required specifications. het convert our question into polar Co-ordinates. cover the For that put y= =rsino from vary Y RYCOS Same region as in our question o should o lo qva. Y and from IT ою Xy Coso -7540 Also Jacobian Yy 9. Sino Y caso - roso trs Sino': Our integral becomes

25G 2²tyr dy dx Facety sng ydyde S. RG are ITL4 Just o dodo J Joando 0 45 10 IT r ² do + 숍 33 (123 풀] : ) T - X 8xAE 452T o becomes 2 189 t fra J s very dydx 4 g 유 aa 3
we have solved the problem.we have converted the Cartesian coordinates to polar coordinates and solved the integral.