What is the integral from 0 to 1 of 2x ?

The integral from 0 to 1 of 2x is 1

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integral from 0 to 1 of 2x

\int_{0}^{1} 2 x d x

1

Solution steps

\int_{0}^{1} 2 x d x

Take the constant out:

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

= 2 \cdot \int_{0}^{1} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2}

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

Simplify

= 1

y = 4^{x + 1}

6 \cdot y^{^{''}} + 2 \cdot y^{^{'}} = 0, y^{^{'}} (0) = 4

\int_{0}^{1} \frac{2 ( x + 2 )}{5} d x

tan (2^{x})

\frac{d}{d x} ((7 x^{2} - 11 x) e^{x})