What is the integral from 1 to 4 of 1/(2sqrt(x)) ?

The integral from 1 to 4 of 1/(2sqrt(x)) is 1

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integral from 1 to 4 of 1/(2sqrt(x))

\int_{1}^{4} \frac{1}{2 x} d x

1

Solution steps

\int_{1}^{4} \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_{1}^{4} \frac{1}{x} d x

Apply the Power Rule

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

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

Apply radical rule:

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

Compute the boundaries:

2

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

Simplify

= 1

\int_{- 1}^{1} (∣ x ∣ - 1) d x

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

\int_{0}^{\frac{π}{2}} \frac{1}{1 + cos ( x )} d x

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

\int_{0}^{2} \frac{x ^{2}}{4} d x

What is the integral from 1 to 4 of 1/(2sqrt(x)) ?
The integral from 1 to 4 of 1/(2sqrt(x)) is 1