In single variable calculus, we used integrals to find the area bounded by two functions say f(x) and g(x) as shown in the diagram below:

Recall also that the area of the shaded region is given by:

From the fundamental Theorem of Calculus, *f(x)- g(x)* can be re-written as:

Where *y (the variable of integration)* could be any other variable apart from *x*.

Now putting (2) in (1) gives:

The above double integral gives the area of the shaded region.

__Worked Example__

Find to 4 decimal places the area of the path of the surface

Solution

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