Evaluate the double integral ∬r(2x−y)da, where r is the region in the first quadrant enclosed by the circle x^2+y^ 2= 4 and the lines x = 0 and y = x, by changing to polar coordinates.

Step-by-step explanation:

We are to integrate the function

over the area enclosed by the circle

Convert into polar coordinates

x=rcost and y = rsint

Since the lines are x=0 and y=x we find that t varies from 0 to pi/4

Double integral will become now

(since variables are independent here)

Substitute for r and t

4 sin pi/4 -2 cospi/4

=

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation: