What is the integral from-3 to 3 of (9t-t^3)(20t) ?

The integral from-3 to 3 of (9t-t^3)(20t) is 1296

Popular >

integral from-3 to 3 of (9t-t^3)(20t)

\int_{- 3}^{3} (9 t - t^{3}) (20 t) d t

1296

Solution steps

\int_{- 3}^{3} (9 t - t^{3}) \cdot 20 t d t

Take the constant out:

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

= 20 \cdot \int_{- 3}^{3} (9 t - t^{3}) t d t

Expand

(9 t - t^{3}) t : 9 t^{2} - t^{4}

= 20 \cdot \int_{- 3}^{3} 9 t^{2} - t^{4} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 20 (\int_{- 3}^{3} 9 t^{2} d t - \int_{- 3}^{3} t^{4} d t)

\int_{- 3}^{3} 9 t^{2} d t = 162

\int_{- 3}^{3} t^{4} d t = \frac{486}{5}

= 20 (162 - \frac{486}{5})

Simplify

20 (162 - \frac{486}{5}) : 1296

= 1296

\int_{0}^{π} 2 sin^{2} (x) d x

\int_{0}^{π} sin (6 x + π) d x

\int_{0.1}^{0.3} e^{- 2 x^{2}} d x

\int_{0}^{6} \frac{x}{64 + x ^{2}} d x

\int_{0}^{1 - x} x cos (y) d z

What is the integral from-3 to 3 of (9t-t^3)(20t) ?
The integral from-3 to 3 of (9t-t^3)(20t) is 1296