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

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- Mar 18th 2006, 12:11 PMfrozenflamesCalculus 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 PMCaptainBlackQuote:

Originally Posted by**frozenflames**

shaded region in the figure.

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 PMfrozenflames
I dont quite understand

- Mar 18th 2006, 01:37 PMCaptainBlackQuote:

Originally Posted by**frozenflames**

RonL