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

1 Answer
Feb 10, 2018

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#]

Explanation:

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