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

The integral from-2 to 0 of sqrt(x/2+1) is 4/3

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integral from-2 to 0 of sqrt(x/2+1)

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

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{1} u \cdot 2 d u

= \int_{0}^{1} u \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int_{0}^{1} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1}

= 2 [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{3}

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

Simplify

= \frac{4}{3}

y^{^{'}} = \frac{x e ^{y}}{y}

t^{2} y^{^{''}} - 4 t y^{^{'}} + 6 y = 0

x \to 0 lim (\frac{2 x}{2 x ^{2}})

\int_{3}^{5} e^{6 x} d x

f (x) = 3 - 2 x

What is the integral from-2 to 0 of sqrt(x/2+1) ?
The integral from-2 to 0 of sqrt(x/2+1) is 4/3