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

The integral from 2 to 4 of 4x^2 is 224/3

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integral from 2 to 4 of 4x^2

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

\frac{224}{3}

Decimal

74.66666 \dots

Solution steps

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

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{2}^{4}

= 4 [\frac{x ^{3}}{3}]_{2}^{4}

Compute the boundaries:

\frac{56}{3}

= 4 \cdot \frac{56}{3}

Simplify

= \frac{224}{3}

\int_{1}^{6} 6 x^{- 4} d x

\int_{\frac{1}{3}}^{5} 1 + 36 x d x

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

\int_{0}^{1} - x^{3} d x

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

What is the integral from 2 to 4 of 4x^2 ?
The integral from 2 to 4 of 4x^2 is 224/3