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

The integral from-1 to 0 of xsqrt(x+1) is -4/15

Popular >

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

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

- \frac{4}{15}

Decimal

- 0.26666 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{1} (u - 1) u d u

= \int_{0}^{1} (u - 1) u d u

Expand

(u - 1) u : u^{\frac{3}{2}} - u

= \int_{0}^{1} u^{\frac{3}{2}} - 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}^{1} u^{\frac{3}{2}} d u - \int_{0}^{1} u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} u d u = \frac{2}{3}

= \frac{2}{5} - \frac{2}{3}

Simplify

\frac{2}{5} - \frac{2}{3} : - \frac{4}{15}

= - \frac{4}{15}

\int_{- \infty}^{- 3} e^{- 2 x} d x

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

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

\int_{0}^{1} x^{2} x^{3} + 3 d x

\int_{- 1}^{1} 3 x^{2} d x

What is the integral from-1 to 0 of xsqrt(x+1) ?
The integral from-1 to 0 of xsqrt(x+1) is -4/15