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

The integral from-1 to 2 of 2xsqrt(2x^2+3) is (11sqrt(11)-5sqrt(5))/3

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integral from-1 to 2 of 2xsqrt(2x^2+3)

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

\frac{11 11 - 5 5}{3}

Decimal

8.43417 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int_{5}^{11} \frac{u}{4} d u

Take the constant out:

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

= 2 \cdot \frac{1}{4} \cdot \int_{5}^{11} u d u

Apply the Power Rule

= 2 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{11}

Simplify

2 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{11} : \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{11}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{11}

Compute the boundaries:

\frac{22 11 - 10 5}{3}

= \frac{1}{2} \cdot \frac{22 11 - 10 5}{3}

Simplify

= \frac{11 11 - 5 5}{3}

What is the integral from-1 to 2 of 2xsqrt(2x^2+3) ?
The integral from-1 to 2 of 2xsqrt(2x^2+3) is (11sqrt(11)-5sqrt(5))/3