Chapter 7.2, Problem 53E

To determine

To state : The given statement is true or false.

Answer to Problem 53E

The given statement is false.

Explanation of Solution

Given information :

The area of the region in the first quadrant enclosed by the graphs of $y=\cos x,y=x$ and the $y-$ axis is given by the integral ${\displaystyle {\int }_0^{0.739}\left(x-\cos x\right)}dx$ .

Consider the given area ${\displaystyle {\int }_0^{0.739}\left(x-\cos x\right)}dx$ .

Find the value of ${\displaystyle {\int }_0^{0.739}\left(x-\cos x\right)}dx$ using maple calculator.

  ${\displaystyle {\int }_0^{0.739}\left(x-\cos x\right)}dx\approx -0.4005$ .

The value of the given integral is negative and it is given that it represents the area of the region in the first quadrant. In first quadrant the values are always positive.

Therefore, the given statement is false.