What is the integral from 0 to 1 of (2a+1)^4 ?

The integral from 0 to 1 of (2a+1)^4 is 121/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of (2a+1)^4

\int_{0}^{1} (2 a + 1)^{4} d a

\frac{121}{5}

Decimal Notation

24.2

Solution steps

\int_{0}^{1} (2 a + 1)^{4} d a

Apply u-substitution

: \int_{1}^{3} \frac{u ^{4}}{2} d u

= \int_{1}^{3} \frac{u ^{4}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{1}^{3} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{1}^{3}

= \frac{1}{2} [\frac{u ^{5}}{5}]_{1}^{3}

Compute the boundaries:

\frac{242}{5}

= \frac{1}{2} \cdot \frac{242}{5}

Simplify

= \frac{121}{5}

\int_{0}^{1} f (t) d t

\int_{1}^{6} \frac{3}{x} d x

\int_{π}^{2 π} θ d θ

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

\int_{0}^{1} (x^{16} + 1 6^{x}) d x

What is the integral from 0 to 1 of (2a+1)^4 ?
The integral from 0 to 1 of (2a+1)^4 is 121/5