Question

Find the area between f(x)=x²+4x and g(x)=x²-6x+5 over the interval 0 less or equal to x or x is less or equal to 1

Answer 1

$$x^2+4x=x^2-6x+5$$

$$x=0.5$$

$$A=\displaystyle\int_{0}^{0.5}(x^2-6x+5-(x^2+4x))dx$$

$$+\displaystyle\int_{0.5}^{1}(x^2+4x-(x^2-6x+5))dx$$

$$=[-5x^2+5x]\begin{matrix} 0.5 \\ 0 \end{matrix}+[5x^2-5x]\begin{matrix} 1 \\ 0.5 \end{matrix}$$

$$=-1.25+2.5+5-5-1.25+2.5$$

$$=2.5({units}^2)$$

Area is 2.5 square units.