What is the integral from-4 to 1 of sqrt(2-x) ?

The integral from-4 to 1 of sqrt(2-x) is 4sqrt(6)-2/3

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integral from-4 to 1 of sqrt(2-x)

\int_{- 4}^{1} 2 - x d x

46 - \frac{2}{3}

Decimal

9.13129 \dots

Solution steps

\int_{- 4}^{1} 2 - x d x

Apply u-substitution

: \int_{6}^{1} - u d u

= \int_{6}^{1} - u d u

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

= - \int_{1}^{6} - u d u

Take the constant out:

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

= - (- \int_{1}^{6} u d u)

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6}

= - (- [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6})

Simplify

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6}

Compute the boundaries:

46 - \frac{2}{3}

= 46 - \frac{2}{3}

\int_{0}^{5} (x - 5)^{2} d x

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

\int_{1}^{10} 1

\int_{0}^{2} (2 x + 3)^{2} d x

\int_{1}^{2} (30 x^{3} + \frac{6}{x ^{2}}) d x

What is the integral from-4 to 1 of sqrt(2-x) ?
The integral from-4 to 1 of sqrt(2-x) is 4sqrt(6)-2/3