Area Bounded by curve

[ZyzzBrah]

Calculate the area of the region bounded by the curves f(x) = cos(x) and \(\displaystyle g(x) = \sqrt{x}\) for \(\displaystyle 0 \le x \le 4\)


here is the graph i ploteed from matlab


Solution:
the left area is
\(\displaystyle \int_{0}^{x}{\cos(x) - \sqrt{x}}\)
the right area is
\(\displaystyle \int_{x}^{4}{\sqrt{x}-\cos{x}}\)

the problem is how do i find the intersection between cos(x) and sqrt(x)?

 

[Deleted member 4993]

Calculate the area of the region bounded by the curves f(x) = cos(x) and \(\displaystyle g(x) = \sqrt{x}\) for \(\displaystyle 0 \le x \le 4\)


here is the graph i ploteed from matlab

View attachment 1541
Solution:
the left area is
\(\displaystyle \int_{0}^{x}{\cos(x) - \sqrt{x}}\)
the right area is
\(\displaystyle \int_{x}^{4}{\sqrt{x}-\cos{x}}\)

the problem is how do i find the intersection between cos(x) and sqrt(x)?

using Newton-Raphson, I get

cos(0.641714371) = √(0.641714371)