What's the area of the first quadrant region bounded by the y-axis, the line y=4-x  and the graph of y=x-cosx?

Area$= 4.93888 \text{ }$square units

Explanation:

Area$= {\int}_{0}^{1.85825} \left[\left(4 - x\right) - \left(x - \cos x\right)\right] \mathrm{dx}$

Area$= {\int}_{0}^{1.85825} \left(4 - 2 x + \cos x\right) \mathrm{dx}$

Area $= \left(4 x - {x}^{2} + \sin x\right)$ Evaluate this integral from $0$ to $1.85825$

Area $= 4 \left(1.85825\right) - {\left(1.85825\right)}^{2} + \sin \left(1.85825\right) - \left(4 \left(0\right) - {0}^{2} + \sin 0\right)$
Area $= 4.93888 \text{ }$square units