What is the integral from 0 to 1 of 6x ?

The integral from 0 to 1 of 6x is 3

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integral from 0 to 1 of 6x

\int_{0}^{1} 6 x d x

3

Solution steps

\int_{0}^{1} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{0}^{1} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{1}

= 6 [\frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= 6 \cdot \frac{1}{2}

Simplify

= 3

y = e^{x}, y = x^{2} - 1, x = - 1, x = 1

n = 1 \sum \infty n e^{6 n}

\frac{d y}{d t} - (\frac{3}{t}) \cdot y = 2 t^{3} e^{2 t}, y (1) = 0

\frac{7}{x}

y^{^{''}} + y = (x^{2} + x) sin (x)