Mister Exam

Integral of lny dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
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 |  log(y) dy
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$$\int\limits_{0}^{1} \log{\left(y \right)}\, dy$$
Integral(log(y), (y, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of a constant is the constant times the variable of integration:

    Now evaluate the sub-integral.

  2. The integral of a constant is the constant times the variable of integration:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
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 | log(y) dy = C - y + y*log(y)
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$$\int \log{\left(y \right)}\, dy = C + y \log{\left(y \right)} - y$$
The graph
The answer [src]
-1
$$-1$$
=
=
-1
$$-1$$
-1
Numerical answer [src]
-1.0
-1.0
The graph
Integral of lny dx

    Use the examples entering the upper and lower limits of integration.