What is the integral from 0 to 1 of 1/(2sqrt(x)) ?

The integral from 0 to 1 of 1/(2sqrt(x)) is 1

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integral from 0 to 1 of 1/(2sqrt(x))

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

1

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{1} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{0}^{1}

= \frac{1}{2} [2 x^{\frac{1}{2}}]_{0}^{1}

Apply radical rule:

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

= \frac{1}{2} [2 x]_{0}^{1}

Compute the boundaries:

2

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

Simplify

= 1

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