What is the integral from pi/6 to pi of |cos(x)| ?

The integral from pi/6 to pi of |cos(x)| is 3/2

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integral from pi/6 to pi of |cos(x)|

\int_{\frac{π}{6}}^{π} ∣ cos (x) ∣ d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{\frac{π}{6}}^{π} ∣ cos (x) ∣ d x

Eliminate Absolutes

= \int_{\frac{π}{6}}^{\frac{π}{2}} cos (x) d x + \int_{\frac{π}{2}}^{π} - cos (x) d x

\int_{\frac{π}{6}}^{\frac{π}{2}} cos (x) d x = \frac{1}{2}

\int_{\frac{π}{2}}^{π} - cos (x) d x = 1

= \frac{1}{2} + 1

Simplify

\frac{1}{2} + 1 : \frac{3}{2}

= \frac{3}{2}

What is the integral from pi/6 to pi of |cos(x)| ?
The integral from pi/6 to pi of |cos(x)| is 3/2