Final answer:
To evaluate the triple integral ∭ Ee^(z/y) dV, where E={(x,y,z): 0≤y≤1,y≤x≤1 ,0≤z≤xy}, set up the integral with respect to x, y, and z and find the limits of integration. Simplify the integral by performing the innermost integration, and then integrate with respect to y and x to find the result.
Step-by-step explanation:
To evaluate the triple integral ∭ Ee^(z/y) dV, where E={(x,y,z): 0≤y≤1,y≤x≤1 ,0≤z≤xy}, we need to set up the integral in terms of x, y, and z and find the limits of integration for each variable. The integral will be ∫01 ∫y1 ∫0xy e^(z/y) dz dy dx.
To solve this integral, we can perform the innermost integral with respect to z. The integral of e^(z/y) with respect to z is e^(z/y) * y, evaluated from 0 to xy. This simplifies the integral to ∫01 ∫y1 y(e^(xy/y) - e^(0/y)) dy dx.
Simplifying further, we have ∫01 ∫y1 y(e^x - 1) dy dx. Finally, we can integrate with respect to y and x to find the result.