What is the integral from 0 to 1 of 1/(sqrt(3y+1)) ?

The integral from 0 to 1 of 1/(sqrt(3y+1)) is 2/3

Popular >

integral from 0 to 1 of 1/(sqrt(3y+1))

\int_{0}^{1} \frac{1}{3 y + 1} d y

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{0}^{1} \frac{1}{3 y + 1} d y

Apply u-substitution

: \int_{1}^{4} \frac{1}{3 u} d u

= \int_{1}^{4} \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{1}^{4} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{1}^{4}

= \frac{1}{3} [2 u^{\frac{1}{2}}]_{1}^{4}

Apply radical rule:

a^{\frac{1}{n}} = n a

= \frac{1}{3} [2 u]_{1}^{4}

Compute the boundaries:

2

= \frac{1}{3} \cdot 2

Simplify

= \frac{2}{3}

\int_{0}^{3} (- x^{2} + 4 x) d x

\int_{0}^{5} (8 e^{0.2 x} + 2 x) d x

\int_{0}^{\frac{π}{5}} sin (5 x) d x

\int_{0}^{2} ln (x^{2} + 1) d x

\int_{0}^{7} 2 x \cdot 3 x + 1 d x

What is the integral from 0 to 1 of 1/(sqrt(3y+1)) ?
The integral from 0 to 1 of 1/(sqrt(3y+1)) is 2/3