TS EAMCET · Maths · Indefinite Integration
Let \(\tan ^0 x=1\). If \(\int\left(\sum_{k=0}^7 \tan ^k x\right) d x=\sum_{k=1}^7 A_k \tan ^k x+C\), then \(\sum_{k=1}^7 A_k\) is equal to
- A 76/25
- B 28/15
- C 38/35
- D 124/75
Answer & Solution
Correct Answer
(B) 28/15
Step-by-step Solution
Detailed explanation
Given, \(\tan ^0 x=1\) \( \int\left(\tan ^0 x+\tan x+\tan ^2 x+\tan ^3 x+\ldots+\tan ^7 x\right) d x= \) \(A_1 \tan x+A_2 \tan ^2 x+\ldots+A_7 \tan ^7 x\) ...(i) If \(I_n=\int \tan ^n x d x \Rightarrow I_n+I_{n-2}=\frac{(\tan x)^{n-1}}{n-1}\) Put…
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