JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(\alpha \in(0,1)\) and \(\beta=\log _{ c }(1-\alpha)\). Let \(P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots . .+\frac{x^n}{n}, x \in(0,1)\) Then the integral \(\int \limits_0^\alpha \frac{ t ^{50}}{1- t } dt\) is equal to
- A \(\beta-P_{50}(\alpha)\)
- B \(-\left(\beta+ P _{50}(\alpha)\right)\)
- C \(P_{50}(\alpha)-\beta\)
- D \(\beta+P_{50}(\alpha)\)
Answer & Solution
Correct Answer
(B) \(-\left(\beta+ P _{50}(\alpha)\right)\)
Step-by-step Solution
Detailed explanation
\(\int \limits_0^\alpha \frac{t^{50}-1+1}{1-t}=-\int \limits_0^\alpha\left(1+t+\ldots . .+ t ^{49}\right)+\int \limits_0^\alpha \frac{1}{1- t } dt\)…
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