What is the integral from 0 to 2 of 6t ?

The integral from 0 to 2 of 6t is 12

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integral from 0 to 2 of 6t

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

12

Solution steps

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

Take the constant out:

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

= 6 \cdot \int_{0}^{2} t d t

Apply the Power Rule

: [\frac{t ^{2}}{2}]_{0}^{2}

= 6 [\frac{t ^{2}}{2}]_{0}^{2}

Compute the boundaries:

2

= 6 \cdot 2

Simplify

= 12

\frac{\partial}{\partial x} (\frac{1}{x - 3})

\frac{\partial}{\partial x} ((2 x - 3 y)^{3})

n = 1 \sum \infty \frac{x ^{2 n}}{n !}

\int \frac{x}{x ^{2} - 2} d x

5 sin (5 t) sin (100 t)