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Popular >

integral from 1 to pi/2 of sqrt(sin(x))

Solution

\int_{1}^{\frac{π}{2}} sin (x) d x

Solution

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

Solution steps

\int_{1}^{\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)]_{1}^{\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} - 1) ∣)

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

Popular Examples

integral from-4 to-1 of (-2x^2-12x-12)

\int_{- 4}^{- 1} (- 2 x^{2} - 12 x - 12) d x

integral from-1 to 0 of 4(e^{1/x})/(x^3)

\int_{- 1}^{0} 4 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

integral from 0 to 1 of-sqrt(x)

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

integral from-4 to 2 of (8-2x-x^2)

\int_{- 4}^{2} (8 - 2 x - x^{2}) d x

integral from 0 to 1 of (x^2+2)e^{-2x}

\int_{0}^{1} (x^{2} + 2) e^{- 2 x} d x

Frequently Asked Questions (FAQ)

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