How to Evaluate Difficult Double Integrals with Limits in the Range of 0 to 1?

[hivesaeed4]

Evaluate ∫∫xexp(xy)dA,
and R (over which the integrand is to be integrated) is {(x,y)|0≤x,y≤1}.
Could someone explain how this is to be done.

 

[tiny-tim]

hi hivesaeed4!

dA = dxdy

try integrating wrt y first ​

 

[hivesaeed4]

My Bad. What I meant was what are the limits we should take for x and y. We are given one limit (either upper or lower limit) in each case. How do we find the second one for both x and y?

 

[tiny-tim]

oh i see!

no, {(x,y)|0≤x,y≤1} is two limits …

the limits apply to both x and y (separately) ​

 

[hivesaeed4]

Look, let me tell you how I see the limits and correct me if I'm wrong.

The lower limit of x is 0. We have to find its upper limit.

The upper limit of y is 1. We have to find its lower limit.

The reason we have to find the upper limit of x and lower limit of y is that they are required for the integration.

Correct?

Also, please tell me how to find the upper limit of x and lower limit of y.

 

[tiny-tim]

no, {(x,y)|0≤x,y≤1} is a shorthand way of saying {(x,y)|0≤x≤1} and {(x,y)|0≤y≤1}

 

[hivesaeed4]

Thanks tiny-tim. Thanks alot. That question had me very confused.