What is the integral from-1 to 3 of 6x(x-1) ?

The integral from-1 to 3 of 6x(x-1) is 32

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integral from-1 to 3 of 6x(x-1)

\int_{- 1}^{3} 6 x (x - 1) d x

32

Solution steps

\int_{- 1}^{3} 6 x (x - 1) d x

Take the constant out:

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

= 6 \cdot \int_{- 1}^{3} x (x - 1) d x

Expand

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

= 6 \cdot \int_{- 1}^{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

= 6 (\int_{- 1}^{3} x^{2} d x - \int_{- 1}^{3} x d x)

\int_{- 1}^{3} x^{2} d x = \frac{28}{3}

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

= 6 (\frac{28}{3} - 4)

Simplify

6 (\frac{28}{3} - 4) : 32

= 32

\int csch^{2} (x) d x

x \to - 3 lim (3 x)

\int 5 x + 3 d x

\frac{\partial}{\partial x} (d y)

128 t - 16 t^{2}, at [4, 5]

What is the integral from-1 to 3 of 6x(x-1) ?
The integral from-1 to 3 of 6x(x-1) is 32