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

The integral from 1 to 3 of (2x^2) is 52/3

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integral from 1 to 3 of (2x^2)

\int_{1}^{3} (2 x^{2}) d x

\frac{52}{3}

Decimal

17.33333 \dots

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{3} x^{2} d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{26}{3}

= 2 \cdot \frac{26}{3}

Simplify

= \frac{52}{3}

\int_{1}^{2} 3 x^{2} + 4 x d x

\int_{- 1}^{1} e^{3 x^{2}} d x

\int_{0}^{2} \frac{1}{2} (e^{x} + e^{- x}) d x

\int_{0}^{π} 2 x sin (2 x^{2}) d x

\int_{0}^{\infty} e^{t x - x} d x

What is the integral from 1 to 3 of (2x^2) ?
The integral from 1 to 3 of (2x^2) is 52/3