Understanding the Point-to-Point Equation in a Book

[giant016]

Homework Statement

I'm just having trouble seeing how the book is getting from point-to-point. I understand the area=height X Width part of the equation, but I don't see how in the seconds step (2i/5)(2/5) turns into [-(2i/5)^2+5](2/5). Smae goes for the second step in the second equation circled in red.

 

[jamesrc]

height is given by f(x) = f(2i/5) so you plug in x=2i/5:
$$f\left(\frac{2i}{5}\right)=-\left(\frac{2i}{5}\right)^2+5$$

same goes for the second equation

you have an expression for x as a function of i that you plug into find f as a function of i.

 

[giant016]

Ahh, now I see. I totally forgot about the f(x)=-x^2 equation. Thanks!