What is the integral from 0 to 3 of (x^2+e^x) ?

The integral from 0 to 3 of (x^2+e^x) is e^3+8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of (x^2+e^x)

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

e^{3} + 8

Decimal

28.08553 \dots

Solution steps

\int_{0}^{3} x^{2} + e^{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}^{3} x^{2} d x + \int_{0}^{3} e^{x} d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} e^{x} d x = e^{3} - 1

= 9 + e^{3} - 1

Simplify

= e^{3} + 8

\int_{3}^{x} \frac{1}{t} d t

\int_{0}^{4} (2 x^{2} + x^{\frac{3}{2}}) d x

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

\int_{\frac{1}{2}}^{\frac{1}{3}} cos (π) x d x

\int_{1}^{x} 2 (1 - \frac{1}{y ^{2}}) d y

What is the integral from 0 to 3 of (x^2+e^x) ?
The integral from 0 to 3 of (x^2+e^x) is e^3+8