Question

Evaluate the integral by interpreting it in terms of areas.

Answer 1

Step 1:

The  integral is  .

Rewrite the integral into two parts .

Evaluate the first part.

Step 2:

Evaluate the second part.

Let .

Since , we can interpret this integral as the area under the curve over the interval  .

Graph the function .

Squaring on each side.

The graph shows that the  is the quarter-circle with radius .

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Solution :

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