What is the integral from-4 to-1 of 4/x ?

The integral from-4 to-1 of 4/x is -8ln(2)

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integral from-4 to-1 of 4/x

\int_{- 4}^{- 1} \frac{4}{x} d x

- 8 ln (2)

Decimal

- 5.54517 \dots

Solution steps

\int_{- 4}^{- 1} \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}^{- 1} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 [ln ∣ x ∣]_{- 4}^{- 1}

Compute the boundaries:

- 2 ln (2)

= 4 (- 2 ln (2))

Simplify

= - 8 ln (2)

\int_{0}^{3} 2 x x^{2} + 16 d x

\int_{4}^{5} x (x^{2} - 16)^{3} d x

\int_{0}^{3} 4 x - x^{2} d x

\int_{2}^{4} (x^{2} + 2) d x

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

What is the integral from-4 to-1 of 4/x ?
The integral from-4 to-1 of 4/x is -8ln(2)