Question

the area of the first quadrant bounded by the y-axis, the line y=4-x, and the graph of y=x-cosx is approximately

Answer 1

The curves $y=4-x$ and $y=x-\cos x$ intersect at approximately $x\approx1.8582$. The area is then

$A\approx\displaystyle\int_0^{1.8582}((4-x)-(x-\cos x))\,\mathrm dx=\int_0^{1.8582}(4-2x+\cos x)\,\mathrm dx\approx4.9389$