# Thread: help with limit

1. ## help with limit

hello,

i am asked to find the double limit of (x^2) e^[y(x^2)] dx dy over the area bounded by y = 1/x and y = 1/(x^2) and x = ln4

thus i need to evaluate the

integral (from x=ln4 to x = infinity) of integral (from y=1/(x^2) to y=1/x) of
(x^2) e^[y(x^2)] dy dx

= integral (from x=ln4 to x = infinity) of (e^x) - e dx

= lim (at t--> infinity) of {(e^t) - et -4 +e ln4} = infinity

am i write?

can someone evaluate the improper integral for me at a slow pace?

Thanks very much!

2. Originally Posted by pepsi
hello,

i am asked to find the double limit of (x^2) e^[y(x^2)] dx dy over the area bounded by y = 1/x and y = 1/(x^2) and x = ln4

thus i need to evaluate the

integral (from x=ln4 to x = infinity) of integral (from y=1/(x^2) to y=1/x) of
(x^2) e^[y(x^2)] dy dx

= integral (from x=ln4 to x = infinity) of (e^x) - e dx

= lim (at t--> infinity) of {(e^t) - et -4 +e ln4} = infinity

am i write?

can someone evaluate the improper integral for me at a slow pace?

Thanks very much!
your solution for integration is correct.

but what do you mean by you asked to find the double limit of $\displaystyle x^2e^{yx^2}$

see this is the area you want

3. Originally Posted by Amer
but what do you mean by you asked to find the double limit of $\displaystyle x^2e^{yx^2}$

i must be sleeping sorry it says the double integral of... i am learning double integrals

p.s. it turns out i was wrong (having seen the answers at the back of the book. I should have known as well because the question asks for the bounded area so the answer is a finite number!

Tx

4. Originally Posted by pepsi
hello,

i am asked to find the double limit of (x^2) e^[y(x^2)] dx dy over the area bounded by y = 1/x and y = 1/(x^2) and x = ln4

thus i need to evaluate the

integral (from x=ln4 to x = infinity) of integral (from y=1/(x^2) to y=1/x) of
(x^2) e^[y(x^2)] dy dx

= integral (from x=ln4 to x = infinity) of (e^x) - e dx

= lim (at t--> infinity) of {(e^t) - et -4 +e ln4} = infinity

am i write?

can someone evaluate the improper integral for me at a slow pace?

Thanks very much!
it will be like this

$\displaystyle \int_{1}^{\ln 4} \int_{\frac{1}{x^2}}^{\frac{1}{x}} x^2 e^{y\cdot x^2 } dy dx$

this is the area after I do zoom to it the red area