# What is the net area between #f(x) = 3-xsqrt(x^2-1) # and the x-axis over #x in [2, 3 ]#?

The area

graph{3-xsqrt(x^2-1) [-1, 5, -7, 3]}

The integration of the constant term is trivial:

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To find the net area between ( f(x) = 3 - x\sqrt{x^2 - 1} ) and the x-axis over ( x ) in the interval ( [2, 3] ), you need to evaluate the definite integral of ( f(x) ) over that interval. The net area is given by the absolute value of the integral:

[ \text{Net Area} = \left| \int_{2}^{3} (3 - x\sqrt{x^2 - 1}) , dx \right| ]

Using calculus techniques, you can integrate the function ( f(x) ) over the interval ( [2, 3] ) to find the net area.

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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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