Question

I had a math problem I solved like this:

In[1]:= Solve[2x(a-x)==0, x]
Out[1]= {{x->0}, {x->a}}

In[2]:= Integrate[2x(a-x), {x,0,a}]
Out[2]= (a^3)/3

In[3]:= Solve[(a^3)/3==a, a]
Out[3]= {{a->0}, {a->-Sqrt[3]}, {a->Sqrt[3]}}

My question is if I could rewrite this to compute it in one step, rather than having to manually input the result from the previous line. I could easily replace the integral used in step three with the Integrate command from step two. But what I can’t figure out is how I would use the result from step 1 as the limits of integration in the integral.

Answer 1

You could combine step 1 and 2 by doing something like

Integrate[2 x (a - x), {x, ##}] & @@ (x /. Solve[2 x (a - x) == 0, x]);