TS EAMCET · Maths · Definite Integration
The positive integer \(n \leq 5\) for which \(\int_0^1 e^x(x-1)^n d x=16-6 e\) is
- A 5
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
It is given that, \(\int_0^1 e^x(x-1)^n d x=16-6 e\) \(\Rightarrow\left[(x-1)^n e^x-n(x-1)^{n-1} e^x+n(n-1)(x-1)^{n-2}\right.\) \(\left.e^x-n(n-1)(n-2)(x-1)^{n-3} e^x+\ldots\right]_0^1=16-6 e\) (on successive integration by parts) As in right hand side coefficient of \(e\) is -6…
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