What is the integral from 0 to pi/2 of |7sin(x)-7cos(2x)| ?

The integral from 0 to pi/2 of |7sin(x)-7cos(2x)| is (21sqrt(3))/2-7

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integral from 0 to pi/2 of |7sin(x)-7cos(2x)|

\int_{0}^{\frac{π}{2}} ∣ 7 sin (x) - 7 cos (2 x) ∣ d x

\frac{21 3}{2} - 7

Decimal Notation

11.18653 \dots

Solution steps

\int_{0}^{\frac{π}{2}} ∣ 7 sin (x) - 7 cos (2 x) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{6}} - 7 sin (x) + 7 cos (2 x) d x + \int_{\frac{π}{6}}^{\frac{π}{2}} 7 sin (x) - 7 cos (2 x) d x

\int_{0}^{\frac{π}{6}} - 7 sin (x) + 7 cos (2 x) d x = \frac{21 3}{4} - 7

\int_{\frac{π}{6}}^{\frac{π}{2}} 7 sin (x) - 7 cos (2 x) d x = \frac{21 3}{4}

= \frac{21 3}{4} - 7 + \frac{21 3}{4}

Simplify

\frac{21 3}{4} - 7 + \frac{21 3}{4} : \frac{21 3}{2} - 7

= \frac{21 3}{2} - 7

y = \frac{2}{x ^{2}}

\int_{6}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{d y}{d t} = 2 - y

\frac{d y}{d x} = x^{4} (32 - x^{5})^{5}

(- 1.6) (1.5)

What is the integral from 0 to pi/2 of |7sin(x)-7cos(2x)| ?
The integral from 0 to pi/2 of |7sin(x)-7cos(2x)| is (21sqrt(3))/2-7