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`