What is the integral from 1 to 3 of 10x(x-1)^3 ?

The integral from 1 to 3 of 10x(x-1)^3 is 104

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 3 of 10x(x-1)^3

\int_{1}^{3} 10 x (x - 1)^{3} d x

104

Solution steps

\int_{1}^{3} 10 x (x - 1)^{3} d x

Take the constant out:

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

= 10 \cdot \int_{1}^{3} x (x - 1)^{3} d x

Expand

x (x - 1)^{3} : x^{4} - 3 x^{3} + 3 x^{2} - x

= 10 \cdot \int_{1}^{3} x^{4} - 3 x^{3} + 3 x^{2} - 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

= 10 (\int_{1}^{3} x^{4} d x - \int_{1}^{3} 3 x^{3} d x + \int_{1}^{3} 3 x^{2} d x - \int_{1}^{3} x d x)

\int_{1}^{3} x^{4} d x = \frac{242}{5}

\int_{1}^{3} 3 x^{3} d x = 60

\int_{1}^{3} 3 x^{2} d x = 26

\int_{1}^{3} x d x = 4

= 10 (\frac{242}{5} - 60 + 26 - 4)

Simplify

10 (\frac{242}{5} - 60 + 26 - 4) : 104

= 104

\int_{3}^{9} 7 d x

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

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

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

\int_{- 1}^{1} t^{2} cos (nπ t) d t

What is the integral from 1 to 3 of 10x(x-1)^3 ?
The integral from 1 to 3 of 10x(x-1)^3 is 104