What is the integral from pi/6 to pi/2 of (sin(x))/x ?

The integral from pi/6 to pi/2 of (sin(x))/x is \Si(pi/2)-\Si(pi/6)

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/2 of (sin(x))/x

\int_{\frac{π}{6}}^{\frac{π}{2}} \frac{sin ( x )}{x} d x

Si (\frac{π}{2}) - Si (\frac{π}{6})

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{2}} \frac{sin ( x )}{x} d x

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= [Si (x)]_{\frac{π}{6}}^{\frac{π}{2}}

Compute the boundaries:

Si (\frac{π}{2}) - Si (\frac{π}{6})

= Si (\frac{π}{2}) - Si (\frac{π}{6})

\int_{1}^{6} ∣ 2 x - 4 ∣ d x

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

\int_{1}^{e} \frac{2 - ln ( x )}{x} d x

\int_{1}^{\infty} arctan (x) d x

\int_{1}^{2} ∣ x ∣ d x

What is the integral from pi/6 to pi/2 of (sin(x))/x ?
The integral from pi/6 to pi/2 of (sin(x))/x is \Si(pi/2)-\Si(pi/6)