|
3.5.9 Manipulating Integrals in Symbolic Form
When Mathematica cannot give you an explicit result for an integral, it leaves the integral in a symbolic form. It is often useful to manipulate this symbolic form.
Mathematica cannot give an explicit result for this integral, so it leaves the integral in symbolic form.
In[1]:= Integrate[x^2 f[x], x]
Out[1]= 
Differentiating the symbolic form gives the integrand back again.
In[2]:= D[%, x]
Out[2]= 
Here is a definite integral which cannot be done explicitly.
In[3]:= Integrate[f[x], {x, a[x], b[x]}]
Out[3]= 
This gives the derivative of the definite integral.
In[4]:= D[%, x]
Out[4]= 
Here is a definite integral with end points that do not explicitly depend on x.
In[5]:= defint = Integrate[f[x], {x, a, b}]
Out[5]= 
The partial derivative of this with respect to u is zero.
In[6]:= D[defint, u]
Out[6]= 
There is a non-trivial total derivative, however.
In[7]:= Dt[defint, u]
Out[7]= 
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | |
