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

The integral from 2 to b of 2x is b^2-4

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integral from 2 to b of 2x

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

b^{2} - 4

Solution steps

\int_{2}^{b} 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_{2}^{b} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{b ^{2}}{2} - 2

= 2 (\frac{b ^{2}}{2} - 2)

Simplify

= b^{2} - 4

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What is the integral from 2 to b of 2x ?
The integral from 2 to b of 2x is b^2-4