What is the integral from 4 to t of (12)/(sqrt(x)) ?

The integral from 4 to t of (12)/(sqrt(x)) is 12(2sqrt(t)-4)

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integral from 4 to t of (12)/(sqrt(x))

\int_{4}^{t} \frac{12}{x} d x

12 (2 t - 4)

Solution steps

\int_{4}^{t} \frac{12}{x} d x

Take the constant out:

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

= 12 \cdot \int_{4}^{t} \frac{1}{x} d x

Apply the Power Rule

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

= 12 [2 x^{\frac{1}{2}}]_{4}^{t}

Apply radical rule:

= 12 [2 x]_{4}^{t}

Compute the boundaries:

2 t - 4

= 12 (2 t - 4)

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What is the integral from 4 to t of (12)/(sqrt(x)) ?
The integral from 4 to t of (12)/(sqrt(x)) is 12(2sqrt(t)-4)