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Popular Calculus >

integral from 1 to x of t

Solution

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

Solution

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

Solution steps

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

Apply the Power Rule

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

Compute the boundaries:

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

= \frac{x ^{2}}{2} - \frac{1}{2}

Simplify

= \frac{x ^{2} - 1}{2}

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Frequently Asked Questions (FAQ)

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