Question

Find the area of the region enclosed by the graphs of f(x)=x³ and g(x)=x²+2x

[Verify your answer by MATHEMATICA and attach the printout of the commands and output]

Answer 1

The area between curves is the area between a curve f(x) and a curve g(x) on an interval [a,b] given by

$A=\smallint_a^b|f(x)-g(x)|dx$

$=\smallint_{-1}^2|x^3-(x^2+2x)|dx$

$=[\frac{x^4}{4}-(\frac{x^3}{3}+x^2)]_{-1}^2$

$Area=\frac{37}{12}$