Question

Find the area between the graphs of f(x) = 3x³ - x² - 10x and g(x)=x² + 2x in the first quadrant of xy-plane (where bothx and y are positive).

Answer 1

we have the functions

`\begin{gathered} f\left(x\right)=3x^(3)-x^(2)-10x \\ g\left(x\right)=x^(2)+2x \end{gathered}`

using a graphing tool

The area between the two graphs in the first quadrant is given by

`\begin{gathered} A=\int_0^(2.361)\left(x^2+2x\right)dx-\int_2^(2.361)\left(3x^3-x^2-10x\right)dx=9.96-1.71 \\ \\ A=8.25\text{ units}^2 \end{gathered}`