What is the integral from 1 to 2 of 2/5 x(x+1) ?

The integral from 1 to 2 of 2/5 x(x+1) is 23/15

integral from 1 to 2 of 2/5 x(x+1)

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

\frac{23}{15}

Decimal

1.53333 \dots

Solution steps

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

Take the constant out:

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

= \frac{2}{5} \cdot \int_{1}^{2} x (x + 1) d x

Expand

x (x + 1) : x^{2} + x

= \frac{2}{5} \cdot \int_{1}^{2} 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

= \frac{2}{5} (\int_{1}^{2} x^{2} d x + \int_{1}^{2} x d x)

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

= \frac{2}{5} (\frac{7}{3} + \frac{3}{2})

Simplify

\frac{2}{5} (\frac{7}{3} + \frac{3}{2}) : \frac{23}{15}

= \frac{23}{15}

x \to 15 lim (\frac{x ^{2}}{5} - \frac{3}{x})

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

y^{^{''}} + 16 y = 16 sec (4 t)

x \to 0 lim (cot (x) arcsin (x))

\int \frac{1}{7 - 2 x} d x

What is the integral from 1 to 2 of 2/5 x(x+1) ?
The integral from 1 to 2 of 2/5 x(x+1) is 23/15