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

The integral from 0 to pi of sqrt(sin(x)) is -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 sqrt(sin(x))

\int_{0}^{π} sin (x) d x

- 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} sin (x) d x

Use the nonelementary integral:

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

y^{^{''}} + y^{^{'}} - 2 y = x^{3} - e^{- x}

\frac{d}{d x} (cos (x) + ln (tan (\frac{x}{2})))

\frac{d}{d y} (ln (x^{2} + y^{2} + z^{2}))

f (x) = ln (2 x + 1)

\frac{x ^{2}}{x - 8}

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