Hello i would like to get a step by step solution to this integrate x^2[e^(x*y)]dx dy, x=0 to x/2, y=0 to 2 but i cant find the way how to do it..Im using WolframAlpha to my mobile.Any ideas?
How can the upper limit of x be x/2 ?
ok lets say that we have to solve this integrate x^2[e^(x*y)]dx dy, x=0 to 1, y=0 to 2 Is it possible to display in WolframAlpha the
solution of integral equation step by step? Not only the final solution. If yes, how to do it?
When in doubt, integrate by parts.
Mathematica and WolframAlpha use very powerful and complicated methods to integrate.
The methods used do not have any steps that a student would use or understand.
There is no way to display the steps used.
In[1]:= Integrate[x^2 Exp[x*y], {x, 0, 1}, {y, 0, 2}]
Out[1]= 1/4 (-1 + E^2)
In[2]:= i1 = Integrate[x^2 Exp[x*y], {y, 0, 2}]
Out[2]= (-1 + E^(2 x)) x
In[3]:= Integrate[i1, {x, 0, 1}]
Out[3]= 1/4 (-1 + E^2)
The only hard integral is x*exp(2*x) which Wolfram Alpha can show step by step:
Take the integral:
integral e^(2 x) x dx
For the integrand e^(2 x) x, integrate by parts, integral f dg = f g- integral g df, where
f = x, dg = e^(2 x) dx,
df = dx, g = e^(2 x)/2:
= 1/2 e^(2 x) x-1/2 integral e^(2 x) dx
For the integrand e^(2 x), substitute u = 2 x and du = 2 dx:
= 1/2 e^(2 x) x-1/4 integral e^u du
The integral of e^u is e^u:
= 1/2 e^(2 x) x-e^u/4+constant
Substitute back for u = 2 x:
= 1/2 e^(2 x) x-e^(2 x)/4+constant
Which is equal to:
Answer: |
| = 1/4 e^(2 x) (2 x-1)+constant
I wasn’t joking when I said “Integrate by Parts”