What is the integral of sqrt(49-x^2)dx from [-7,7]?

#int_-7^7sqrt(49-x^2)dx#

Answer 1

Without even doing integration, I can tell you it will be

#49/2pi#

The graph of #y =sqrt(49 - x^2)# is a semi-circle of radius #7#. We know that a definite integral is a measure of area, therefore, we seek to find the area under the semi circle (from #x= -7# to #x = +7#, which is the entire semi-circle).

#A = (7^2pi)/2 = 49/2pi " " u^2#

We can see from the graph that it indeed is a semi-circle of radius #7#.

Hopefully this helps!

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Answer from HIX Tutor

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.

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.

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