What is the integral from 0 to pi of (8e^x+9sin(x)) ?

The integral from 0 to pi of (8e^x+9sin(x)) is 8e^pi+10

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to pi of (8e^x+9sin(x))

\int_{0}^{π} (8 e^{x} + 9 sin (x)) d x

8 e^{π} + 10

Decimal

195.12554 \dots

Solution steps

\int_{0}^{π} 8 e^{x} + 9 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}^{π} 8 e^{x} d x + \int_{0}^{π} 9 sin (x) d x

\int_{0}^{π} 8 e^{x} d x = 8 (e^{π} - 1)

\int_{0}^{π} 9 sin (x) d x = 18

= 8 (e^{π} - 1) + 18

Simplify

8 (e^{π} - 1) + 18 : 8 e^{π} + 10

= 8 e^{π} + 10

\int_{0}^{1} \frac{1}{1 + e ^{x - 1}} d x

\int_{0}^{2} (- x^{2} + 3 x - 2) d x

\int_{50}^{100} \frac{x}{16 + 8 x ^{2}} d x

\int_{0}^{t} x sin (t - x) d x

\int_{0}^{2} 10 x^{2} d x

What is the integral from 0 to pi of (8e^x+9sin(x)) ?
The integral from 0 to pi of (8e^x+9sin(x)) is 8e^pi+10