What is the integral from 0 to 1 of h(x-x^2) ?

The integral from 0 to 1 of h(x-x^2) is 1/6 h

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 h(x-x^2)

\int_{0}^{1} h (x - x^{2}) d x

\frac{1}{6} h

Solution steps

\int_{0}^{1} h (x - x^{2}) d x

Take the constant out:

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

= h \cdot \int_{0}^{1} x - x^{2} 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

= h (\int_{0}^{1} x d x - \int_{0}^{1} x^{2} d x)

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= h (\frac{1}{2} - \frac{1}{3})

Join

\frac{1}{2} - \frac{1}{3} : \frac{1}{6}

= \frac{1}{6} h

\int_{2 x}^{x^{2}} t^{2} + 1 d t

\int_{0}^{\frac{1}{3}} x ln (3 x) d x

\int_{2}^{5} \frac{1}{( x - 2 ) ^{4}} d x

\int_{0}^{\frac{π}{2}} x cos (7 x) d x

\int_{1}^{2} (2 x - 1)^{4} d x

What is the integral from 0 to 1 of h(x-x^2) ?
The integral from 0 to 1 of h(x-x^2) is 1/6 h