# Calculus Problem

• Mar 18th 2006, 12:11 PM
frozenflames
Calculus Problem
83. What is the area of the region in the first quadrant enclosed by the graphs of y = cosx, y = x,and the y-axis?

(A) 0.127
(B) 0.385
(C) 0.400
(D) 0.600
(E) 0.947
• Mar 18th 2006, 01:20 PM
CaptainBlack
Quote:

Originally Posted by frozenflames
83. What is the area of the region in the first quadrant enclosed by the graphs of y = cosx, y = x,and the y-axis?

(A) 0.127
(B) 0.385
(C) 0.400
(D) 0.600
(E) 0.947

First sketch the required area, see attachment. The required area is the

Just counting squares indicates that the area is close to 0.4, but we
will find this area by integration. This is:

$\displaystyle \int_0^{x_1} \cos(x)-x\ dx$

where $\displaystyle x_1$ is the solution of $\displaystyle \cos(x)=x$ in $\displaystyle [0,1]$.
Now using the bisection method gives that $\displaystyle x_1\approx 0.739$

So we seek:

$\displaystyle \int_0^{0.739} \cos(x)-x\ dx=\left[\sin(x)-x^2/2\right]_0^{0.739}=0.400$

RonL
• Mar 18th 2006, 01:27 PM
frozenflames
I dont quite understand
• Mar 18th 2006, 01:37 PM
CaptainBlack
Quote:

Originally Posted by frozenflames
I dont quite understand

I had not finished typing the solution so look again

RonL