Question

What is the result of the double exponential integral ∫∫ e^(xy) dxdy?

a) e
b) 1
c) xy
d) e^(x²y²)

Answer 1

The result of the double exponential integral ∫∫ e^(xy) dxdy is d) e^(x²y²).

Step-by-step explanation:

The double exponential integral can be solved using integration by parts. Let's start by rewriting the integral as:

∫∫ e^(xy) dxdy

We can integrate the inner integral with respect to x first:

∫ e^(xy) dx = (1/y) * e^(xy) + C

Now, we can integrate the outer integral with respect to y:

∫ [(1/y) * e^(xy) + C] dy = (1/y²) * e^(xy) + C * y + D

Since there are no limits given for the integral, the result will be an indefinite integral.

So, the correct option is d) e^(x²y²).