What is the net area between #f(x) = x^2+1/x # and the x-axis over #x in [2, 4 ]#?

Answer 1

Charles Anctil

The area is given by the integral

#A=int_2^4 (x^2+1/x)dx=[x^3/3+lnx]_2^4=56/3+ln2=19.36#

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Answer 2

Cameron Alexander

To find the net area between the function ( f(x) = x^2 + \frac{1}{x} ) and the x-axis over ( x ) in the interval ([2, 4]), we integrate the absolute value of the function over that interval. Thus, the net area is given by:

[ \int_{2}^{4} |x^2 + \frac{1}{x}| , dx ]

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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.

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