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

The integral from pi/6 to pi of sin(x) is 1+(sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{\frac{π}{6}}^{π} sin (x) d x

1 + \frac{3}{2}

Decimal Notation

1.86602 \dots

Solution steps

\int_{\frac{π}{6}}^{π} sin (x) d x

Use the common integral:

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

= [- cos (x)]_{\frac{π}{6}}^{π}

Compute the boundaries:

1 + \frac{3}{2}

= 1 + \frac{3}{2}

- \frac{8}{( 1 + 4 x ) ^{2}}

\int \frac{1}{2} + \frac{1}{2} cos (2 x) d x

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

x^{4} - 2 x^{4}

\int \frac{x}{x ^{2} + x - 2} d x

What is the integral from pi/6 to pi of sin(x) ?
The integral from pi/6 to pi of sin(x) is 1+(sqrt(3))/2