Question

Find the area of the closed region bounded by the curve y=x^2-x and the x-axis

Answer 1

This one of those types of problems where it's really difficult to visual the quadratic function unless you can remember back to algebra.

Mind you, it's not completely necessary, but being able to visualize the graph can help quite a bit when you're trying to grasp these concepts.

So back in algebra, or maybe pre-calc, I forget which, we would put a parabola into STANDARD form, making it easier to graph.

So let's complete the square on the quadratic. We'll add and subtract 1 from the right side.\[\large y=x^2-x+1-1 \qquad \rightarrow \qquad y=(x-1)^2-1\]So now in standard form, we can see that this parabola has a vertex at (1,-1) making it easier to draw.