What is the integral from 0 to 2 of ln(x) ?

The integral from 0 to 2 of ln(x) is 2ln(2)-2

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integral from 0 to 2 of ln(x)

\int_{0}^{2} ln (x) d x

2 ln (2) - 2

Solution steps

\int_{0}^{2} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{2}

= [x ln (x) - \int 1 d x]_{0}^{2}

\int 1 d x = x

= [x ln (x) - x]_{0}^{2}

Compute the boundaries:

2 ln (2) - 2

= 2 ln (2) - 2

\int_{0}^{\frac{π}{2}} cos^{8} (x) d x

f (t) = t^{3} - 9 t^{2} + 24 t

\int \frac{x}{( x ^{3} - 1 )} d x

y^{^{''}} + 16 y = 3 sin (8 t), y (0) = 0, y^{^{'}} (0) = 0

\frac{\partial}{\partial y} (\frac{3 x - 3 y}{3 x + 3 y})

What is the integral from 0 to 2 of ln(x) ?
The integral from 0 to 2 of ln(x) is 2ln(2)-2