What is the integral from 1 to 3 of 5x^2 ?

The integral from 1 to 3 of 5x^2 is 130/3

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integral from 1 to 3 of 5x^2

\int_{1}^{3} 5 x^{2} d x

\frac{130}{3}

Decimal Notation

43.33333 \dots

Solution steps

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

Apply the Power Rule

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

= 5 [\frac{x ^{3}}{3}]_{1}^{3}

Compute the boundaries:

\frac{26}{3}

= 5 \cdot \frac{26}{3}

Simplify

= \frac{130}{3}

\int_{0}^{1} x (x + 1)^{- 3} d x

\int_{0}^{1} 1 + u^{2} d u

\int_{0}^{π} 2 sin (x) - sin (2 x) d x

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

\int_{π}^{2 π} cos (θ) d θ

What is the integral from 1 to 3 of 5x^2 ?
The integral from 1 to 3 of 5x^2 is 130/3