What is the integral from 1 to 4 of ln(y) ?

The integral from 1 to 4 of ln(y) is 8ln(2)-3

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integral from 1 to 4 of ln(y)

\int_{1}^{4} ln (y) d y

8 ln (2) - 3

Decimal

2.54517 \dots

Solution steps

\int_{1}^{4} ln (y) d y

Apply Integration By Parts

: [y ln (y) - \int 1 d y]_{1}^{4}

= [y ln (y) - \int 1 d y]_{1}^{4}

\int 1 d y = y

= [y ln (y) - y]_{1}^{4}

Compute the boundaries:

8 ln (2) - 3

= 8 ln (2) - 3

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

\int_{- 1}^{4} (2 - 2 x) d x

\int_{0}^{2} 3 y d y

\int_{- l n (\frac{1}{2})}^{l n (2)} e^{2 x} d x

\int_{a}^{b} f (a + b - x) d x

What is the integral from 1 to 4 of ln(y) ?
The integral from 1 to 4 of ln(y) is 8ln(2)-3