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

The integral from 1 to 4 of (4x^2) is 84

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integral from 1 to 4 of (4x^2)

\int_{1}^{4} (4 x^{2}) d x

84

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

Compute the boundaries:

21

= 4 \cdot 21

Simplify

= 84

What is the integral from 1 to 4 of (4x^2) ?
The integral from 1 to 4 of (4x^2) is 84