how to solve these questions??
 

There are 2 questions which seem quite simple at first glance but i'm unable to solve them..the first one is question No:5(a) paper-I ce 2013 exam and the second 5b..

Question 5a asks for calculating volume while double integral is given.... so how double integral can give volume?? what is also perplexing is that we have 2 coordinate(x and y): axis so how volume can be computed in 2d??


Question 5b: in this question the examiner asks for line integral over the closed surface, in my opinion we have to parameterize this...but im having no idea how to do this....

kindly help me in this regard....

i would suggest to refer the verctor and tensor analysis book by dr. nawazish ali. I havn't started the chapter yet but such tricky questions are answered over there.
By the way what are you optionals Mr. Ummad

i have studied nawazish's book it doesn't contain these sort of problems...my optional's are applied maths, psychology, us history and journalism....

Dear Ummad Zafar. 5a in Paper of AM-2013, is a volume because, we need to say the integrand is Z. Simply compute the double integral 0<=x<=2 and x^2<=y<=2x. If you are still confuse, I am on my profile.
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5b is simple close curve that encloses the area between line y=2x and parabola y=x^2. From origin to intersection, y=x^2 => dy/dx=2x, Now compute the integral by replacing dy with 2xdx. For return do the same. Pardon I am not a good teacher. Just shared what I knew.