What is the integral from-3 to 0 of xsqrt(x+3) ?

The integral from-3 to 0 of xsqrt(x+3) is (18sqrt(3))/5-6sqrt(3)

Popular >

integral from-3 to 0 of xsqrt(x+3)

\int_{- 3}^{0} x x + 3 d x

\frac{18 3}{5} - 63

Decimal Notation

- 4.15692 \dots

Solution steps

\int_{- 3}^{0} x x + 3 d x

Apply u-substitution

: \int_{0}^{3} (u - 3) u d u

= \int_{0}^{3} (u - 3) u d u

Expand

(u - 3) u : u^{\frac{3}{2}} - 3 u

= \int_{0}^{3} u^{\frac{3}{2}} - 3 u d u

Apply the Sum Rule:

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

= \int_{0}^{3} u^{\frac{3}{2}} d u - \int_{0}^{3} 3 u d u

\int_{0}^{3} u^{\frac{3}{2}} d u = \frac{18 3}{5}

\int_{0}^{3} 3 u d u = 63

= \frac{18 3}{5} - 63

\int_{0}^{1} 9 e^{3 x} d x

\int_{0}^{l n (a)} 4 e^{2 x} d x

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

\int_{1}^{e} \frac{( 3 + ln ( x ) ) ^{2}}{x} d x

\int_{0}^{1} 2 t^{3} 4 t^{2} + 4 d t

What is the integral from-3 to 0 of xsqrt(x+3) ?
The integral from-3 to 0 of xsqrt(x+3) is (18sqrt(3))/5-6sqrt(3)