What is the integral from pi/3 to pi of sin(x+pi/3) ?

The integral from pi/3 to pi of sin(x+pi/3) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from pi/3 to pi of sin(x+pi/3)

\int_{\frac{π}{3}}^{π} sin (x + \frac{π}{3}) d x

0

Solution steps

\int_{\frac{π}{3}}^{π} sin (x + \frac{π}{3}) d x

Apply u-substitution

= \int_{\frac{2 π}{3}}^{π + \frac{π}{3}} sin (u) d u

Use the common integral:

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

= [- cos (u)]_{\frac{2 π}{3}}^{π + \frac{π}{3}}

Compute the boundaries:

0

= 0

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

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

\int_{0}^{1} x^{2} 1 + x^{2} d x

\int_{- π}^{π} x^{4} sin (x) d x

\int_{0}^{\frac{1}{2}} sin (π x) d x

What is the integral from pi/3 to pi of sin(x+pi/3) ?
The integral from pi/3 to pi of sin(x+pi/3) is 0