Question

Help with the calculus problem please

Answer 1

The area of the region is equal to the area under the curve y = cos(x) over the interval 0 ≤ x ≤ π/6, given by the integral

$\displaystyle\int_0^{\frac\pi6}\cos(x)\,\mathrm dx = \sin(x)\bigg|_0^{\frac\pi6}=\sin\left(\frac\pi6\right)-\sin(0)=\boxed{\frac12}$

which follows from

• the fact that d/dx [sin(x)] = cos(x)

• the fundamental theorem of calculus