What is the integral from 0 to pi/2 of (e^t+cos(t)) ?

The integral from 0 to pi/2 of (e^t+cos(t)) is e^{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/2 of (e^t+cos(t))

\int_{0}^{\frac{π}{2}} (e^{t} + cos (t)) d t

e^{\frac{π}{2}}

Decimal Notation

4.81047 \dots

Solution steps

\int_{0}^{\frac{π}{2}} e^{t} + cos (t) d t

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}} e^{t} d t + \int_{0}^{\frac{π}{2}} cos (t) d t

\int_{0}^{\frac{π}{2}} e^{t} d t = e^{\frac{π}{2}} - 1

\int_{0}^{\frac{π}{2}} cos (t) d t = 1

= e^{\frac{π}{2}} - 1 + 1

Simplify

= e^{\frac{π}{2}}

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

\int_{0}^{\frac{1}{2}} (2 x + 1) e^{x} d x

\int_{3}^{4} \frac{1}{25 - x ^{2}} d x

\int_{0}^{4} k x d x

\int_{1}^{4} - 2 x + 8 d x

What is the integral from 0 to pi/2 of (e^t+cos(t)) ?
The integral from 0 to pi/2 of (e^t+cos(t)) is e^{pi/2}