# What is a double integral?

The easiest way to think of a double integral is as the volume under a surface in 3-dimensional space. This is analogous to thinking of a normal integral as being the area under a curve.

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A double integral is an integral with two variables. It extends the concept of a single integral, which computes the area under a curve, to finding the volume under a surface in three-dimensional space or the mass of a two-dimensional region with varying density. It represents the cumulative effect of a function over a region in a two-dimensional space. The notation for a double integral over a region (R) of a function (f(x, y)) is typically written as (\iint_R f(x, y) , dA), where (dA) represents an infinitesimal area element.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the indefinite integral of #int x/(sqrt(9-x^2))#?
- How do you integrate #f(x) = 2x+4x^3+6x^5+...+2nx^(2n-1)+...# ?
- How do you evaluate the integral #int 1/(x+1)^(1/3)dx# from -2 to 0?
- How do you integrate #(sec(x)^2-1)(sin(x)/cos(x))#?
- How do you evaluate the definite integral #int sqrt(2/x)dx# from [1,8]?

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