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

The integral from 0 to 2 of 2x is 4

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integral from 0 to 2 of 2x

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

4

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

2

= 2 \cdot 2

Simplify

= 4

\frac{s + 5}{s ^{2} + 6 s + 18}

y^{^{''}} - 6 y^{^{'}} + 9 y = 6 x^{2} + 2 - 12 e^{3 x}

(3 + sin (2 x))^{2}, at x = 0

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

\int 2 x + 8 x^{- 2} d x