Question

Find the area of the region bounded by the graphs of y=
\sqrt{x} and y= -x - 1 between x=1 and x=4.

Answer 1

so graph the functions

use

https://www.desmos.com/calculator

but you are basically find the area between



the area below the x axis needs absolute values... so its basically the sum of 2 areas 1 above and 1 below the x asxis

so its

\[A = \int\limits_{1}^{4} (x^{\frac{1}{2}}) dx + \left| \int\limits_{1}^{4} (-x -1)dx \right|\]

hope it helps