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

The integral from 1 to 2 of 4x^2 is 28/3

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integral from 1 to 2 of 4x^2

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

\frac{28}{3}

Decimal Notation

9.33333 \dots

Solution steps

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

Apply the Power Rule

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

= 4 [\frac{x ^{3}}{3}]_{1}^{2}

Compute the boundaries:

\frac{7}{3}

= 4 \cdot \frac{7}{3}

Simplify

= \frac{28}{3}

x \to 5 - lim (f (x))

\frac{d}{d x} (ln (\frac{x ^{3} - 4}{x}))

x \to 0 lim (\frac{ln ( x )}{x + 1})

f (x) = \frac{7 x}{x - 3}, at x = 6

2 + 5 tan^{- 1} (\frac{x}{2})

What is the integral from 1 to 2 of 4x^2 ?
The integral from 1 to 2 of 4x^2 is 28/3