Mister Exam

Integral of lnt dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |  log(t) dt
 |           
/            
0            
$$\int\limits_{0}^{1} \log{\left(t \right)}\, dt$$
Integral(log(t), (t, 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]
  /                            
 |                             
 | log(t) dt = C - t + t*log(t)
 |                             
/                              
$$\int \log{\left(t \right)}\, dt = C + t \log{\left(t \right)} - t$$
The graph
The answer [src]
-1
$$-1$$
=
=
-1
$$-1$$
-1
Numerical answer [src]
-1.0
-1.0
The graph
Integral of lnt dx

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