Questions
Multiple fill-in-the-blank
(a) Integrate the following (i) (Hint: You may substitute , and adopt integration by parts) [2 marks](ii) (Hint: You may let , , use and adopt integration by parts)[2 marks] (b) Differentiate [3 marks][Fill in the blank]
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Step-by-Step Analysis
The question has two parts (a) and (b), with blank spaces to fill. The provided answers are the intended completions for each blank.
Part (a) (i): Evaluate ∫ x e^x dx. A standard approach is integration by parts or recognizing a derivative pattern. If we set up integration by parts with u = x and dv = e^x dx, then du = dx and v = e^x, giving ∫ x e^x dx = x e^x − ∫ e^x dx = x e^x − e^x + C = (x − 1) e^x + C. The given fill [(x - 1)e^{x}] matches exactly this result, so it is correct.
Part (a) (ii)......Login to view full explanationLog in for full answers
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