What is the integral from 1 to 2 of 21t^2 ?

The integral from 1 to 2 of 21t^2 is 49

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integral from 1 to 2 of 21t^2

\int_{1}^{2} 21 t^{2} d t

49

Solution steps

\int_{1}^{2} 21 t^{2} d t

Take the constant out:

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

= 21 \cdot \int_{1}^{2} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{1}^{2}

= 21 [\frac{t ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= 21 \cdot \frac{7}{3}

Simplify

= 49

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What is the integral from 1 to 2 of 21t^2 ?
The integral from 1 to 2 of 21t^2 is 49