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Evaluate the integral by interpreting it in terms of areas.

0 votes

Evaluate the integral by interpreting it in terms of areas.

asked Jan 23, 2015 in CALCULUS by anonymous

1 Answer

0 votes

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 .

image

image.

Solution :

image.

answered Jan 29, 2015 by yamin_math Mentor
edited Jan 29, 2015 by yamin_math

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