Read through all the steps below carefully:
- We know from the product rule that dxd(uv)=dxdvu+dxduv.
- Integrate both sides with respect to x to get uv=∫u dv+∫ v du⟹∫u dv=uv−∫v du.
- Consider ∫12xdx.
- Define u=x1 and dv=dx.
- Then, du=−x2dx and v=x.
- Substitute the variables into the equation in step 2 to get ∫12xdx=1+∫12xdx.
- Subtract both sides of the equation in step 6 by ∫12xdx to get 0=1.
In which of these steps did I first make a mistake by using flawed logic?
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