What is the integral from pi/6 to (5pi)/6 of sin(x) ?

The integral from pi/6 to (5pi)/6 of sin(x) is square root of 3

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integral from pi/6 to (5pi)/6 of sin(x)

\int_{\frac{π}{6}}^{\frac{5 π}{6}} sin (x) d x

3

Decimal Notation

1.73205 \dots

Solution steps

\int_{\frac{π}{6}}^{\frac{5 π}{6}} sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= [- cos (x)]_{\frac{π}{6}}^{\frac{5 π}{6}}

Compute the boundaries:

3

= 3

\int_{- 3}^{3} (3 x^{3} - 2 x^{2} + x + 1) d x

\int_{- \infty}^{4} 3 e^{- 3 x} d x

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

\int_{- 1}^{0} (2 x + 1)^{3} d x

\int_{1}^{2} (\frac{1}{y} + \frac{2}{3}) d y

What is the integral from pi/6 to (5pi)/6 of sin(x) ?
The integral from pi/6 to (5pi)/6 of sin(x) is square root of 3