Posted by **maga** on Monday, April 2, 2012 at 12:48am.

evaluate the double integral

∫R∫ lny/x dA

for the region R is the rectangle defined by 1<x<e^2 and 1<y<e

- calculus -
**Steve**, Monday, April 2, 2012 at 11:35am
∫[1,e^2]∫[1,e] lny/x dy dx

= ∫[1,e^2](y/x (lny - 1))[1,e] dx

= ∫[1,e^2] [(e/x (1-1))-(1/x (0-1))] dx

= ∫[1,e^2] 1/x dx

= lnx [1,e^2]

= 2

## Answer this Question

## Related Questions

- calculus - evaluate the double integral ∫R∫ ye^x^3 dA for the region...
- calculus - Suppose R is the rectangle 1<=x<=4, |y|<=2 and evaluate the ...
- Calculus - Evaluate the triple integral ∫∫∫_E (x+y)dV where E ...
- Calculus - Evaluate the triple integral ∫∫∫_E (x)dV where E is...
- Calculus - Evaluate the triple integral ∫∫∫_E (xy)dV where E ...
- Calculus - Evaluate the triple integral ∫∫∫_E (z)dV where E is...
- Calculus - Evaluate the triple integral ∫∫∫_E (xyz)dV where E ...
- Calculus - Evaluate the following definite integral: integral at a = -1, b=2 -...
- Calculus 2 correction - I just wanted to see if my answer if correct the ...
- Calculus - Evaluate the triple integral ∫∫∫_E (x^2.e^y)dV ...