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

The integral from 1 to t of 2x is t^2-1

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integral from 1 to t of 2x

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

t^{2} - 1

Solution steps

\int_{1}^{t} 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_{1}^{t} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{t ^{2}}{2} - \frac{1}{2}

= 2 (\frac{t ^{2}}{2} - \frac{1}{2})

Simplify

= t^{2} - 1

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What is the integral from 1 to t of 2x ?
The integral from 1 to t of 2x is t^2-1