What is the integral from 0 to 4 of ln(t) ?

The integral from 0 to 4 of ln(t) is 8ln(2)-4

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integral from 0 to 4 of ln(t)

\int_{0}^{4} ln (t) d t

8 ln (2) - 4

Decimal

1.54517 \dots

Solution steps

\int_{0}^{4} ln (t) d t

Apply Integration By Parts

: [t ln (t) - \int 1 d t]_{0}^{4}

= [t ln (t) - \int 1 d t]_{0}^{4}

\int 1 d t = t

= [t ln (t) - t]_{0}^{4}

Compute the boundaries:

8 ln (2) - 4

= 8 ln (2) - 4

\int_{0}^{π} 1 - cos (2 x) d x

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

\int_{0}^{2} 1 - x^{2} d x

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

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

What is the integral from 0 to 4 of ln(t) ?
The integral from 0 to 4 of ln(t) is 8ln(2)-4