What is the integral from 0 to 3 of 2x(x-7) ?

The integral from 0 to 3 of 2x(x-7) is -45

Popular >

integral from 0 to 3 of 2x(x-7)

\int_{0}^{3} 2 x (x - 7) d x

- 45

Solution steps

\int_{0}^{3} 2 x (x - 7) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{3} x (x - 7) d x

Expand

x (x - 7) : x^{2} - 7 x

= 2 \cdot \int_{0}^{3} x^{2} - 7 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

= 2 (\int_{0}^{3} x^{2} d x - \int_{0}^{3} 7 x d x)

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 7 x d x = \frac{63}{2}

= 2 (9 - \frac{63}{2})

Simplify

2 (9 - \frac{63}{2}) : - 45

= - 45

\int_{x}^{π} sin (y^{2}) d y

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

\int_{0}^{l} x sin^{2} (\frac{2 π x}{l}) d x

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

\int_{0}^{3} x^{2} - 2 x + 3 d x

What is the integral from 0 to 3 of 2x(x-7) ?
The integral from 0 to 3 of 2x(x-7) is -45