What is the integral from 0 to pi/2 of (6+3sin(x)) ?

The integral from 0 to pi/2 of (6+3sin(x)) is 3pi+3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi/2 of (6+3sin(x))

\int_{0}^{\frac{π}{2}} (6 + 3 sin (x)) d x

3 π + 3

Decimal

12.42477 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 6 + 3 sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{π}{2}} 6 d x + \int_{0}^{\frac{π}{2}} 3 sin (x) d x

\int_{0}^{\frac{π}{2}} 6 d x = 3 π

\int_{0}^{\frac{π}{2}} 3 sin (x) d x = 3

= 3 π + 3

What is the integral from 0 to pi/2 of (6+3sin(x)) ?
The integral from 0 to pi/2 of (6+3sin(x)) is 3pi+3