What is the integral from-5 to 0 of 2+sqrt(4-x)+x ?

The integral from-5 to 0 of 2+sqrt(4-x)+x is 61/6

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integral from-5 to 0 of 2+sqrt(4-x)+x

\int_{- 5}^{0} 2 + 4 - x + x d x

\frac{61}{6}

Decimal Notation

10.16666 \dots

Solution steps

\int_{- 5}^{0} 2 + 4 - x + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 5}^{0} 2 d x + \int_{- 5}^{0} 4 - x d x + \int_{- 5}^{0} x d x

\int_{- 5}^{0} 2 d x = 10

\int_{- 5}^{0} 4 - x d x = \frac{38}{3}

\int_{- 5}^{0} x d x = - \frac{25}{2}

= 10 + \frac{38}{3} - \frac{25}{2}

Simplify

10 + \frac{38}{3} - \frac{25}{2} : \frac{61}{6}

= \frac{61}{6}

\int_{1}^{4} \frac{lo g _{2} ( x )}{x} d x

\int_{1}^{4} x + 6 d x

\int_{1}^{e} (24 + ln (x))^{2} d x

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

\int_{0}^{1} e^{x} e^{x} + 4 d x

What is the integral from-5 to 0 of 2+sqrt(4-x)+x ?
The integral from-5 to 0 of 2+sqrt(4-x)+x is 61/6