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

The integral from-2 to 3 of 2xsqrt(2x^2-3) is (5(3sqrt(15)-sqrt(5)))/3

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

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

\frac{5 ( 3 15 - 5 )}{3}

Decimal

15.63813 \dots

Solution steps

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

Apply u-substitution

= 2 \cdot \int_{5}^{15} \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}^{15} u d u

Apply the Power Rule

= 2 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{15}

Simplify

2 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{15} : \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{15}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{15}

Compute the boundaries:

1015 - \frac{10 5}{3}

= \frac{1}{2} (1015 - \frac{10 5}{3})

Simplify

= \frac{5 ( 3 15 - 5 )}{3}

What is the integral from-2 to 3 of 2xsqrt(2x^2-3) ?
The integral from-2 to 3 of 2xsqrt(2x^2-3) is (5(3sqrt(15)-sqrt(5)))/3