Answer to Question #338647 in Calculus for Nhlabathi nonhlanh

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.