integral from 0 to 2 of x^6 — step-by-step solution

Let's compute the integral:

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

ⓘ An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1:

\int x^{6} d x

\frac{x^{7}}{7}

▷

\frac{x^{7}}{7}

Let's evaluate over the interval

[0, 2]

\frac{2^{7}}{7} - \frac{0^{7}}{7}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

2^{7}

2 \cdot ... \cdot 2

, 7 times =

128

\frac{128}{7} + 0

ⓘ Adding 0 changes nothing:

\frac{128}{7} + 0

\frac{128}{7}

▶Integral:

\frac{128}{7}

The numeric value of:

\frac{128}{7}

equals:

▷

\approx 18.2857