What is 'C' in the following reaction sequence?
Step 1: Understanding the Reaction Sequence - The given reaction sequence involves a Grignard reagent (CH\(_3\)MgBr) reacting with a ketone (Propanone) in an ether medium.
- Adding CH\(_3\)MgBr to Propanone gives an alcohol intermediate (A).
- Hydrolysis using H\(_3\)O\(^+\) leads to the formation of 2-methyl-2-propanol (B).
- The final step involves heating with Cu at 573 K, which results in dehydration, forming an alkene as the final product C.
Step 2: Identifying the Product - The alcohol undergoes elimination to form 2-methylprop-1-ene as the final product.
Step 3: Correct Answer Thus, the correct answer is 2-methylprop-1-ene.
If \[ \int e^x (x^3 + x^2 - x + 4) \, dx = e^x f(x) + C, \] then \( f(1) \) is: