Question

Please quickly and clear  

Given 11, 6**** 1x2 + y2 dydx. Rewrite the integral in polar coordinates. Select one: radrde O b. Card ST S" Srdr ST rdrde rPdrdo O d.

Answer 1

in polar coordinates x = rcos$\small \theta$

and y = rsin$\small \theta$

x² + y² = r²

$\small \sqrt{x^{2}+y^{2}} =r$ denotes the upper half of semicircle

y axis (0.1) theta = pi/2 (-1,0) (1,0) theta =0 theta = pi x axis (0,-1) theta =3pi/2

and for upper half of circle r varies from 0 to 1 and theta varies from 0 to pi

when varies from x = 1 to -1 theta varies from 0 to pi

so the double integration changes

$\small \int_{0}^{\pi }\int_{0}^{1}r^{2} dr d\theta$

option d is correct