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_{- 1}^{1} \frac{1}{∣ x ∣} d x

\int_{2}^{8} 3 x d x

\int_{0}^{\frac{π}{4}} 7 sec (x) tan (x) d x

\int_{0}^{1} 30 x (2 x^{2} + 1)^{4} d x

\int_{- 6}^{1} (2 x + 6) d x

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