What is the integral from 0 to pi of 2sqrt(sin(x)) ?

The integral from 0 to pi of 2sqrt(sin(x)) is 2(-2\E(2*1/2 (pi/2-pi)\vert)+2\E(2*1/2 (pi/2-0)\vert))

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integral from 0 to pi of 2sqrt(sin(x))

\int_{0}^{π} 2 sin (x) d x

2 (- 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - π) ∣) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣))

Solution steps

\int_{0}^{π} 2 sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{π} sin (x) d x

Use the nonelementary integral:

\int sin (x) d x = - 2 E (\frac{1}{2} (\frac{π}{2} - x) ∣ 2)

= 2 [- 2 E (\frac{1}{2} (\frac{π}{2} - x) ∣ 2)]_{0}^{π}

Compute the boundaries:

- 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - π) ∣) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

= 2 (- 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - π) ∣) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣))

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What is the integral from 0 to pi of 2sqrt(sin(x)) ?
The integral from 0 to pi of 2sqrt(sin(x)) is 2(-2\E(2*1/2 (pi/2-pi)\vert)+2\E(2*1/2 (pi/2-0)\vert))