Math Help - Confirmation of Right Answer of Area Between Curves

1. Confirmation of Right Answer of Area Between Curves

Is the answer between curves of this equations
y=2x-7
y=x^2+4x-7 equal to 8/3 check please! thanks

2. Hello, v3ndetta!

I got a different answer . . .

Is the area between the curves: . $\begin{Bmatrix}y\:=\:2x-7 \\ y\:=\:x^2+4x-7\end{Bmatrix}$ . equal to $\frac{8}{3}$ ?

They intersect when: . $2x-7 \:=\:x^2+4x-7$

. . $x^2+2x \:=\:0 \quad\Rightarrow\quad x(x+2)\:=\:0 \quad\Rightarrow\quad x \:=\:-2,\:0$

The line is above the parabola over this interval

. . so we have: . $A \;=\;\int^0_{-2}\bigg[(2x-7) - (x^2+4x-7)\bigg]\,dx \;=\;\int^{\,0}_{\text{-}2}(-x^2-2x)\,dx$

. . $= \;-\frac{x^3}{3} - x^2\,\bigg]^0_{-2} \;=\;(0 - 0) - \left(\tfrac{8}{3} - 4\right) \;=\;-\left(-\tfrac{4}{3}\right) \;=\;\boxed{\frac{4}{3}}$

3. thanks very much! lifesaver