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Popular >

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

Solution

\int_{0}^{\frac{x}{2}} sin (x) d x

Solution

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

Solution steps

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

Compute the boundaries:

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

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

Popular Examples

integral from 1 to infinity of 8/(x^5)

\int_{1}^{\infty} \frac{8}{x ^{5}} d x

integral from-pi/9 to pi/9 of sec^3(3x)

\int_{- \frac{π}{9}}^{\frac{π}{9}} sec^{3} (3 x) d x

integral from 4 to 14 of 1/x

\int_{4}^{14} \frac{1}{x} d x

integral from-1 to 1 of (8x^2-1)^2

\int_{- 1}^{1} (8 x^{2} - 1)^{2} d x

integral from-pi to 0 of x-pi

\int_{- π}^{0} x - π d x

Frequently Asked Questions (FAQ)

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