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### Assignment 5

Calculate the area which is enclosed by the circle , that is a circle with center and radius .

### Solution

The area of the circle can be calculated by first calculating the area of the circle in the first quadrant and multiply it by . The function in the first quadrant is:

and thus we have to calculate:

First we apply the substitution method:

, with ranging from to

which results in:

Now we use a formula from trigonometry:

and thus:

Then the integral becomes:

The area of the whole circle is thus . This is the result we already knew.

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