What is the integral from 0 to 1 of (3t-1)^{50} ?

The integral from 0 to 1 of (3t-1)^{50} is (2^{51}+1)/(153)

Popular >

integral from 0 to 1 of (3t-1)^{50}

\int_{0}^{1} (3 t - 1)^{50} d t

\frac{2 ^{51} + 1}{153}

Decimal Notation

1.47176 E 13

Solution steps

\int_{0}^{1} (3 t - 1)^{50} d t

Apply u-substitution

: \int_{- 1}^{2} \frac{u ^{50}}{3} d u

= \int_{- 1}^{2} \frac{u ^{50}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- 1}^{2} u^{50} d u

Apply the Power Rule

: [\frac{u ^{51}}{51}]_{- 1}^{2}

= \frac{1}{3} [\frac{u ^{51}}{51}]_{- 1}^{2}

Compute the boundaries:

\frac{2 ^{51}}{51} + \frac{1}{51}

= \frac{1}{3} (\frac{2 ^{51}}{51} + \frac{1}{51})

Simplify

= \frac{2 ^{51} + 1}{153}

x \to \infty lim (\frac{x}{4})

x \to 0 lim (\frac{x}{x ^{2} - 3 x})

\frac{\partial}{\partial y} (\frac{7 y}{x ^{5}})

\frac{d}{d x} ((\frac{1 + 3 x}{3 x}) (3 - x))

\int sin^{3} (4 x) cos (4 x) d x

What is the integral from 0 to 1 of (3t-1)^{50} ?
The integral from 0 to 1 of (3t-1)^{50} is (2^{51}+1)/(153)