What is the integral from 1 to 3 of 2/t ?

The integral from 1 to 3 of 2/t is 2ln(3)

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integral from 1 to 3 of 2/t

\int_{1}^{3} \frac{2}{t} d t

2 ln (3)

Decimal

2.19722 \dots

Solution steps

\int_{1}^{3} \frac{2}{t} d t

Take the constant out:

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

= 2 \cdot \int_{1}^{3} \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= 2 [ln ∣ t ∣]_{1}^{3}

Compute the boundaries:

ln (3)

= 2 ln (3)

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

\int_{0}^{π} 4 sin (x) - sin (4 x) d x

\int_{0}^{\infty} \frac{3}{x} d x

\int_{0}^{3} (x^{2} - 2 x - 3) d x

\int_{0}^{\frac{π}{3}} x cos (3 x) d x

What is the integral from 1 to 3 of 2/t ?
The integral from 1 to 3 of 2/t is 2ln(3)