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

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

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

\int_{0}^{\frac{π}{2}} sin (x) d x

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

Solution steps

\int_{0}^{\frac{π}{2}} 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}^{\frac{π}{2}}

Compute the boundaries:

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

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

\int_{1}^{4} (- x^{2} + 5 x - 4) d x

\int_{1}^{2} \frac{x ^{2} + 1}{x ^{3}} d x

\int_{1}^{2} (5 x - 1) d x

\int_{- 1}^{1} x^{2} x^{3} d x

\int_{- 1}^{1} (x^{2} + x + 2) d x

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