What is the integral from 2 to 4 of 5x^2 ?

The integral from 2 to 4 of 5x^2 is 280/3

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integral from 2 to 4 of 5x^2

\int_{2}^{4} 5 x^{2} d x

\frac{280}{3}

Decimal Notation

93.33333 \dots

Solution steps

\int_{2}^{4} 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int_{2}^{4} x^{2} d x

Apply the Power Rule

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

= 5 [\frac{x ^{3}}{3}]_{2}^{4}

Compute the boundaries:

\frac{56}{3}

= 5 \cdot \frac{56}{3}

Simplify

= \frac{280}{3}

f (x) = 4 - x^{2}, at x = - 4

\int \frac{10}{x} + 10 x d x

x \to - 2 + lim (\frac{∣ x + 2 ∣}{x + 2})

\int \frac{x + 11}{x ^{2} + 16 x + 68} d x

x \to 1 lim (x^{2} + 3 x)

What is the integral from 2 to 4 of 5x^2 ?
The integral from 2 to 4 of 5x^2 is 280/3