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

The integral from 0 to pi of sqrt(sin(θ)) 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(θ))

\int_{0}^{π} sin (θ) d θ

- 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 (θ) d θ

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} - θ) ∣ 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) ∣)

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\int_{0}^{1} x^{6} e^{- x} d x

\int_{0}^{1} x^{7} e^{- x} d x

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\int_{0}^{1} (1 - x^{4})^{3} d x

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