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

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

Popular >

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

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

- \frac{4}{3}

Solution steps

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

Apply u-substitution

: \int_{0}^{1} 2 (u^{2} - 1) d u

= \int_{0}^{1} 2 (u^{2} - 1) 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^{2} - 1 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

= 2 (\int_{0}^{1} u^{2} d u - \int_{0}^{1} 1 d u)

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

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

= 2 (\frac{1}{3} - 1)

Simplify

2 (\frac{1}{3} - 1) : - \frac{4}{3}

= - \frac{4}{3}

\int_{1}^{2} sin (2 θ) cos (3 θ) d θ

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

\int_{0}^{1} x^{3} (4 + x^{4})^{3} d x

\int_{0}^{2} - 2 t + 2 d t

\int_{0}^{2} 8^{x} d x

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