What is the integral from-1 to 1 of (x^3-(3x)/5)^2 ?

The integral from-1 to 1 of (x^3-(3x)/5)^2 is 8/175

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 1 of (x^3-(3x)/5)^2

\int_{- 1}^{1} (x^{3} - \frac{3 x}{5})^{2} d x

\frac{8}{175}

Solution steps

\int_{- 1}^{1} (x^{3} - \frac{3 x}{5})^{2} d x

Expand

(x^{3} - \frac{3 x}{5})^{2} : x^{6} - \frac{6 x ^{4}}{5} + \frac{9 x ^{2}}{25}

= \int_{- 1}^{1} x^{6} - \frac{6 x ^{4}}{5} + \frac{9 x ^{2}}{25} 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_{- 1}^{1} x^{6} d x - \int_{- 1}^{1} \frac{6 x ^{4}}{5} d x + \int_{- 1}^{1} \frac{9 x ^{2}}{25} d x

\int_{- 1}^{1} x^{6} d x = \frac{2}{7}

\int_{- 1}^{1} \frac{6 x ^{4}}{5} d x = \frac{12}{25}

\int_{- 1}^{1} \frac{9 x ^{2}}{25} d x = \frac{6}{25}

= \frac{2}{7} - \frac{12}{25} + \frac{6}{25}

Simplify

\frac{2}{7} - \frac{12}{25} + \frac{6}{25} : \frac{8}{175}

= \frac{8}{175}

\int_{0}^{1} 8 x^{2} + 1 d x

\int_{x}^{1} 6 x yz d z

\int_{0}^{2} 1

\int_{3}^{6} \frac{x}{x - 2} d x

\int_{9}^{100} 1 x^{- 2} d x

What is the integral from-1 to 1 of (x^3-(3x)/5)^2 ?
The integral from-1 to 1 of (x^3-(3x)/5)^2 is 8/175