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

Answer 1

#3/4#

The problem can be expressed in terms of an integral like so

#int_1^2(2x^-3)dx#

Integrate using power rules

#-x^-2# from #1->2#
#-(2)^-2--(1)^-2#
#1-1/4 rarr 3/4#
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Answer 2

To find the net area between ( f(x) = \frac{2}{x^3} ) and the x-axis over ( x ) in the interval ([1, 2]), you need to calculate the definite integral of ( f(x) ) from 1 to 2 and take the absolute value of the result. Since the function ( f(x) ) is above the x-axis in this interval, you don't need to subtract any area. Therefore, the net area is simply the integral of ( f(x) ) over the given interval.

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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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