What is the integral from 0 to pi/2 of |6sin(x)-6cos(2x)| ?

The integral from 0 to pi/2 of |6sin(x)-6cos(2x)| is 9sqrt(3)-6

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integral from 0 to pi/2 of |6sin(x)-6cos(2x)|

\int_{0}^{\frac{π}{2}} ∣ 6 sin (x) - 6 cos (2 x) ∣ d x

93 - 6

Decimal

9.58845 \dots

Solution steps

\int_{0}^{\frac{π}{2}} ∣ 6 sin (x) - 6 cos (2 x) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{6}} - 6 sin (x) + 6 cos (2 x) d x + \int_{\frac{π}{6}}^{\frac{π}{2}} 6 sin (x) - 6 cos (2 x) d x

\int_{0}^{\frac{π}{6}} - 6 sin (x) + 6 cos (2 x) d x = - 6 (- \frac{3}{2} + 1) + \frac{3 3}{2}

\int_{\frac{π}{6}}^{\frac{π}{2}} 6 sin (x) - 6 cos (2 x) d x = 33 + \frac{3 3}{2}

= - 6 (- \frac{3}{2} + 1) + \frac{3 3}{2} + 33 + \frac{3 3}{2}

Simplify

- 6 (- \frac{3}{2} + 1) + \frac{3 3}{2} + 33 + \frac{3 3}{2} : 93 - 6

= 93 - 6

What is the integral from 0 to pi/2 of |6sin(x)-6cos(2x)| ?
The integral from 0 to pi/2 of |6sin(x)-6cos(2x)| is 9sqrt(3)-6