What is the integral from 0 to pi of (8e^x+5sin(x)) ?

The integral from 0 to pi of (8e^x+5sin(x)) is 8e^pi+2

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+5sin(x))

\int_{0}^{π} (8 e^{x} + 5 sin (x)) d x

8 e^{π} + 2

Decimal

187.12554 \dots

Solution steps

\int_{0}^{π} 8 e^{x} + 5 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} 5 sin (x) d x

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

\int_{0}^{π} 5 sin (x) d x = 10

= 8 (e^{π} - 1) + 10

Simplify

8 (e^{π} - 1) + 10 : 8 e^{π} + 2

= 8 e^{π} + 2

\int_{1}^{2} 4 r^{4} ln (r) d r

y = 2 x + 1

y^{^{'}} + \frac{3}{x} y = 0, y (1) = 5

f (x) = e^{x} 1 + x^{2}

\frac{d}{d x} (ln (x^{2} + 2 - y))

What is the integral from 0 to pi of (8e^x+5sin(x)) ?
The integral from 0 to pi of (8e^x+5sin(x)) is 8e^pi+2