What is the integral from 1 to 2y of y/x ?

The integral from 1 to 2y of y/x is yln(2|y|)

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integral from 1 to 2y of y/x

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

y ln (2 ∣ y ∣)

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= y [ln ∣ x ∣]_{1}^{2 y}

Compute the boundaries:

ln (2 ∣ y ∣)

= y ln (2 ∣ y ∣)

3 cos (2 x)

x \to 2 lim (6 x - 2)

\int_{0}^{3} x + 1 d x

n = 0 \sum \infty \frac{9}{4} (\frac{1}{4})^{n}

tan (x), 3

What is the integral from 1 to 2y of y/x ?
The integral from 1 to 2y of y/x is yln(2|y|)