What is the integral from-2 to 0 of xsqrt(2x^2+1) ?

The integral from-2 to 0 of xsqrt(2x^2+1) is -13/3

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integral from-2 to 0 of xsqrt(2x^2+1)

\int_{- 2}^{0} x 2 x^{2} + 1 d x

- \frac{13}{3}

Decimal

- 4.33333 \dots

Solution steps

\int_{- 2}^{0} x 2 x^{2} + 1 d x

Apply u-substitution

: \int_{9}^{1} \frac{u}{4} d u

= \int_{9}^{1} \frac{u}{4} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{9} \frac{u}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int_{1}^{9} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

= - \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{9}

Compute the boundaries:

\frac{52}{3}

= - \frac{1}{4} \cdot \frac{52}{3}

Simplify

= - \frac{13}{3}

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\int_{1}^{5} \frac{1}{96} x y d y

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

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

What is the integral from-2 to 0 of xsqrt(2x^2+1) ?
The integral from-2 to 0 of xsqrt(2x^2+1) is -13/3