- 4

- 0

I tried mathematica but the I didn't get the same answer :( Is this precision problem or something else?

Code:

```
In[79]:= Collect[
Sum[Integrate[LegendreP[i, x]*Sin[2 x], {x, -1, 1}]/
Integrate[LegendreP[i, x]^2, {x, -1, 1}]*LegendreP[i, x], {i, 0,
3}], x] // N
Out[79]= 1.94378 x - 1.06264 x^3
In[80]:= Collect[
Sum[Integrate[
1/Sqrt[1 - x^2] ChebyshevT[i, x]*Sin[2 x], {x, -1, 1}]/
Integrate[1/Sqrt[1 - x^2] ChebyshevT[i, x]^2, {x, -1, 1}]*
ChebyshevT[i, x], {i, 0, 3}], x] // N
Out[80]= 1.92711 x - 1.03155 x^3
```