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Intégrales doubles

What is a double integral?
In fact, this is also the definition of a double integral, or more exactly an integral of a function of two variables over a rectangle. Here is the official definition of a double integral of a function of two variables over a rectangular region R R as well as the notation that we’ll use for it.
What is y y in a double integral?
For a given value of x x, y y ranges from 0 to x/2 x / 2, as illustrated above by the vertical dashed line from (x, 0) ( x, 0) to (x, x/2) ( x, x / 2). In a double integral, the outer limits must be constant, but the inner limits can depend on the outer variable.
What is the difference between inner and Outer Limits of a double integral?
In a double integral, the outer limits must be constant, but the inner limits can depend on the outer variable. This means, we must put y y as the inner integration variables, as was done in the second way of computing Example 1. The only difference from Example 1 is that the upper limit of y y is x/2 x / 2. The double integral is
What are definite integrals for functions of single variables?
Before starting on double integrals let’s do a quick review of the definition of definite integrals for functions of single variables. First, when working with the integral, we think of x x ’s as coming from the interval a ≤ x ≤ b a ≤ x ≤ b. For these integrals we can say that we are integrating over the interval a ≤ x ≤ b a ≤ x ≤ b.

What is a double integral?