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How to find area of the function: f(x)=e^3, g(x)=x^3 , x=0 and x=1?

I don't really understand the "e" part.
Thanks <3

Answer 1

Isaiah Allen

Area #approx 19.835537# sq units
[Assuming you mean the area bounded by:
#f(x)=e^3, g(x)=x^3, x=0 and x=1#]

I assume you mean the area bounded by: #f(x)=e^3, g(x)=x^3, x=0 and x=1#

First note that #e# is a constant #approx 2.718282#

So #e^3 approx 20.085537#

Then the area bounded by #f(x)=e^3, x=0 and x=1# and the #x-#axis is a rectangle with sides #approx 20.085537 and 1#

Hence this rectangle has an area of #approx 20.085537# sq units.

So, the area bounded by: #f(x)=e^3, g(x)=x^3, x=0 and x=1# will equal:

#approx 20.085537 - int_0^1 x^3 dx#

#approx 20.085537 - x^4/4|_0^1#

#approx 20.085537 - 0.25#

#approx 19.835537# sq units

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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.

How to find area of the function: f(x)=e^3, g(x)=x^3 , x=0 and x=1?

I don't really understand the "e" part. Thanks <3

I don't really understand the "e" part.
Thanks <3