What is the integral from 4 to 36 of 4/(sqrt(x)) ?

The integral from 4 to 36 of 4/(sqrt(x)) is 32

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integral from 4 to 36 of 4/(sqrt(x))

\int_{4}^{36} \frac{4}{x} d x

32

Solution steps

\int_{4}^{36} \frac{4}{x} d x

Take the constant out:

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

= 4 \cdot \int_{4}^{36} \frac{1}{x} d x

Apply the Power Rule

: [2 x^{\frac{1}{2}}]_{4}^{36}

= 4 [2 x^{\frac{1}{2}}]_{4}^{36}

Apply radical rule:

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

= 4 [2 x]_{4}^{36}

Compute the boundaries:

8

= 4 \cdot 8

Simplify

= 32

\int_{2}^{4} x^{2} - 6 x + 8 d x

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\int_{2}^{4} 6 x^{2} - 6 x - 1 d x

What is the integral from 4 to 36 of 4/(sqrt(x)) ?
The integral from 4 to 36 of 4/(sqrt(x)) is 32