Double integrals

Double integrals

A double integral is an integral of two variable function f(x,y) over a region R If R=[a, b] × [c, d] then the double integral can be done by iterated Integration( integrate first with respect to y and then with respect to x )

The notation used for double integral is  

Here the function f(x,y) is integrated with respect to y first and treat f(x) constant and then integrate with respect to x and apply limits of x and simplify

Example 7.23

Solutions:

Let us first integrate with respect to y and then with respect to x. Hence the double integral is written as

Example 7.24

Solution:

Example 7.25

Solution: