What is the integral from 0 to 3 of (3t-1)^{54} ?

The integral from 0 to 3 of (3t-1)^{54} is (8^{55}+1)/(165)

Popular >

integral from 0 to 3 of (3t-1)^{54}

\int_{0}^{3} (3 t - 1)^{54} d t

\frac{8 ^{55} + 1}{165}

Decimal Notation

2.83443 E 47

Solution steps

\int_{0}^{3} (3 t - 1)^{54} d t

Apply u-substitution

: \int_{- 1}^{8} \frac{u ^{54}}{3} d u

= \int_{- 1}^{8} \frac{u ^{54}}{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}^{8} u^{54} d u

Apply the Power Rule

: [\frac{u ^{55}}{55}]_{- 1}^{8}

= \frac{1}{3} [\frac{u ^{55}}{55}]_{- 1}^{8}

Compute the boundaries:

\frac{8 ^{55}}{55} + \frac{1}{55}

= \frac{1}{3} (\frac{8 ^{55}}{55} + \frac{1}{55})

Simplify

= \frac{8 ^{55} + 1}{165}

\int_{0}^{3} t d t

\int_{0}^{1} \frac{1}{1 + 4 x ^{2}} d x

\int_{0}^{6} 4 x - x^{2} d x

\int_{0}^{2} 8 - x^{3} d x

\int_{1}^{3} 4 x^{3} - 3 x^{2} + 1 d x

What is the integral from 0 to 3 of (3t-1)^{54} ?
The integral from 0 to 3 of (3t-1)^{54} is (8^{55}+1)/(165)