That would be written as (m+n^2)(m-n^2)
Answer:
![\int_{-1}^{1}7(x^{3}-x)\:dx](https://tex.z-dn.net/?f=%5Cint_%7B-1%7D%5E%7B1%7D7%28x%5E%7B3%7D-x%29%5C%3Adx)
Step-by-step explanation:
1) The other curve is
then the common points of both curves are x-intercepts, the roots of ![y=7(x^{3}-x)](https://tex.z-dn.net/?f=y%3D7%28x%5E%7B3%7D-x%29)
![y=7(x^{3}-x)\Rightarrow 7(x^3-x)=0 \Rightarrow 7(x^{3}-x)=7x(x-1)(x-1)\Rightarrow \\S=\left ( 0,0 \right ),\left ( -1,0 \right ),\left ( 1,0 \right )](https://tex.z-dn.net/?f=y%3D7%28x%5E%7B3%7D-x%29%5CRightarrow%207%28x%5E3-x%29%3D0%20%5CRightarrow%207%28x%5E%7B3%7D-x%29%3D7x%28x-1%29%28x-1%29%5CRightarrow%20%5C%5CS%3D%5Cleft%20%28%200%2C0%20%5Cright%20%29%2C%5Cleft%20%28%20-1%2C0%20%5Cright%20%29%2C%5Cleft%20%28%201%2C0%20%5Cright%20%29)
2). Then those intersection points are the upper and the lower limits. Plugging in to this formula for they belong to the interval [-1,1]:
![\int_{a}^{b}|f(x)-g(x)dx](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%7Cf%28x%29-g%28x%29dx)
![\int_{a}^{b}|f(x)-g(x)dx \Rightarrow \int_{-1}^{1}|7(x^{3}-x)-0|dx \Rightarrow \int_{-1}^{1}7(x^{3}-x)\:dx](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%7Cf%28x%29-g%28x%29dx%20%5CRightarrow%20%5Cint_%7B-1%7D%5E%7B1%7D%7C7%28x%5E%7B3%7D-x%29-0%7Cdx%20%5CRightarrow%20%5Cint_%7B-1%7D%5E%7B1%7D7%28x%5E%7B3%7D-x%29%5C%3Adx)
Answer:
33 1/3
Step-by-step explanation:
25/1 * 4/3 =
100/3 = 33.3... or 33 1/3