What is the integral from 1 to 3 of pi/y ?

The integral from 1 to 3 of pi/y is piln(3)

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integral from 1 to 3 of pi/y

\int_{1}^{3} \frac{π}{y} d y

π ln (3)

Decimal

3.45139 \dots

Solution steps

\int_{1}^{3} \frac{π}{y} d y

Take the constant out:

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

= π \cdot \int_{1}^{3} \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= π [ln ∣ y ∣]_{1}^{3}

Compute the boundaries:

ln (3)

= π ln (3)

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\int_{0}^{1} 10 x 5^{x} d x

\int_{2}^{4} 7 x ln (x) d x

What is the integral from 1 to 3 of pi/y ?
The integral from 1 to 3 of pi/y is piln(3)