Question

What is the area enclosed by the graph of

y = x2 + x – 2

 below the x-axis?

 

Answer 1

we have equation

$y = x^2 + x – 2$

we have to get the area below the x-axis ,see the graph below to get better idea

this part of parabola is required area

so we have to solve the integral $\int_{-1}^{2}x^2-x+2 dx \\$

$=[\frac{x^3}{3}-\frac{x^2}{2}+2x]_{-1}^{2}=\frac{-9}{2}=-4.5$

taking mod the answer is 4.5 unit$^2$