What is the net area between #f(x) = xlnx-xe^x # and the x-axis over #x in [2, 4 ]#?
#=[1/4x^2(2 ln x -1 )-e^x(x-1)]@, between the limits x = 2 and 4.
Upon substitution of limits and simplification, this
The graph inserted is suitably scaled to revveal the relevant portion of the curve
graph{x(ln x-e^x) [0, 4, -300, -0]}
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To find the net area between the function ( f(x) = x\ln(x) - xe^x ) and the x-axis over ( x ) in the interval ( [2, 4] ), you need to compute the definite integral of ( f(x) ) from 2 to 4. The net area is the absolute value of this integral.
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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.
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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