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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

  1. A 76/25
  2. B 28/15
  3. C 38/35
  4. D 124/75
Verified Solution

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…