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Help with the calculus problem please

Help with the calculus problem please-example-1

1 Answer

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The area of the region is equal to the area under the curve y = cos(x) over the interval 0 ≤ xπ/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

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