What is the integral from 1 to 4 of 3x^2 ?

The integral from 1 to 4 of 3x^2 is 63

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integral from 1 to 4 of 3x^2

\int_{1}^{4} 3 x^{2} d x

63

Solution steps

\int_{1}^{4} 3 x^{2} d x

Take the constant out:

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

= 3 \cdot \int_{1}^{4} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{1}^{4}

= 3 [\frac{x ^{3}}{3}]_{1}^{4}

Compute the boundaries:

21

= 3 \cdot 21

Simplify

= 63

\int_{1}^{9} (2 x + \frac{1}{x}) d x

\int_{0}^{2} \frac{x ^{2}}{x ^{3} + 1} d x

\int_{0}^{4} \frac{1}{9 - 2 x} d x

\int_{0}^{x} \frac{1}{x ^{2} + y ^{2}} d y

\int_{- 2}^{2} 4 - y^{2} d y

What is the integral from 1 to 4 of 3x^2 ?
The integral from 1 to 4 of 3x^2 is 63