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

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

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

\int_{1}^{a} (\frac{1}{4 x}) d x

a - 1

Solution steps

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

Apply Integration By Parts

: [\frac{1}{2} x - \int - \frac{1}{4 x ^{\frac{1}{2}}} d x]_{1}^{a}

= [\frac{1}{2} x - \int - \frac{1}{4 x ^{\frac{1}{2}}} d x]_{1}^{a}

\int - \frac{1}{4 x ^{\frac{1}{2}}} d x = - \frac{1}{2} x^{\frac{1}{2}}

= [\frac{1}{2} x - (- \frac{1}{2} x^{\frac{1}{2}})]_{1}^{a}

Simplify

[\frac{1}{2} x - (- \frac{1}{2} x^{\frac{1}{2}})]_{1}^{a} : [\frac{1}{2} (x + x)]_{1}^{a}

= [\frac{1}{2} (x + x)]_{1}^{a}

Compute the boundaries:

a - 1

= a - 1

e^{s i n (x)} cos (x)

x \to - 1 lim (\frac{x + 1}{6 x ^{2} + 3 + 3 x})

\int 2 x sec^{2} (3 x) d x

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

\frac{d}{d x} f (x) = 3 x^{2} - 5 x + 2

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