JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let \({I_n} = \smallint {\tan ^n}xdx,\left( {n > 1} \right).\) \({I_4} + {I_6} = a{\tan ^5}x + b{x^5} + C\), where \(C\) is constant of integration , then ordered pair \(\left( {a,b} \right)\) equal to :
- A \(\left( { - \frac{1}{5},0} \right)\)
- B \(\left( { - \frac{1}{5},1} \right)\)
- C \(\left( {\frac{1}{5},0} \right)\)
- D \(\left( {\frac{1}{5}, - 1} \right)\)
Answer & Solution
Correct Answer
(C) \(\left( {\frac{1}{5},0} \right)\)
Step-by-step Solution
Detailed explanation
\(I_{n}=\int \tan ^{n} x d x, n>1\) \(\text { Let } \mathrm{I}=\mathrm{I}_{4}+\mathrm{I}_{6}\) \(=\int\left(\tan ^{4} x+\tan ^{6} x\right) d x\) \(=\int \tan ^{4} x \sec ^{2} x d x\) \(\text { Let } \tan x=t\) \(\Rightarrow \sec ^{2} x d x=d t\) \(\therefore I=\int t^{4} d t\)…
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