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Download Integration using Trigonometric Identities MCQs Free PDF

Integration using Trigonometric Identities MCQ Quiz in తెలుగు - Objective Question with Answer for Integration using Trigonometric Identities - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Last updated on Apr 5, 2025

పొందండి Integration using Trigonometric Identities సమాధానాలు మరియు వివరణాత్మక పరిష్కారాలతో బహుళ ఎంపిక ప్రశ్నలు (MCQ క్విజ్). వీటిని ఉచితంగా డౌన్‌లోడ్ చేసుకోండి Integration using Trigonometric Identities MCQ క్విజ్ Pdf మరియు బ్యాంకింగ్, SSC, రైల్వే, UPSC, స్టేట్ PSC వంటి మీ రాబోయే పరీక్షల కోసం సిద్ధం చేయండి.

Latest Integration using Trigonometric Identities MCQ Objective Questions

Integration using Trigonometric Identities Question 1:

\(\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} \mathrm{~d} x=\)

  1. \(\frac{1}{2} \log \left|\frac{\cos x}{3 \sin x+4 \cos x}\right|+c\)
  2. \(\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c\)
  3. \(\frac{1}{3} \log \left|\frac{3 \cos x+\sin x}{3 \cos x+4 \sin x}\right|+c\)
  4. \(\frac{1}{2} \log \left|\frac{\cos x+4 \sin x}{3 \cos x+4 \sin x}\right|+c\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c\)

Integration using Trigonometric Identities Question 1 Detailed Solution

Integration using Trigonometric Identities Question 2:

∫(tan7 x + tan x)dx =

  1. \(\frac{\tan ^2 x}{12}\left(2 \tan ^4 x-3 \tan ^2 x+6\right)+c\)
  2. \(\frac{\tan ^2 x}{6}-\frac{\tan ^5 x}{4}+\frac{\tan ^4 x}{2}+c\)
  3. \(\frac{\tan ^2 x}{6}\left(\tan ^4 x+3 \tan ^2 x+4\right)+c\)
  4. \(\frac{\tan x}{12}\left(\tan ^4 x-3 \tan ^2 x+6\right)+c\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{\tan ^2 x}{12}\left(2 \tan ^4 x-3 \tan ^2 x+6\right)+c\)

Integration using Trigonometric Identities Question 2 Detailed Solution

Top Integration using Trigonometric Identities MCQ Objective Questions

Integration using Trigonometric Identities Question 3:

\(\int \frac{\operatorname{cosec} x}{3 \cos x+4 \sin x} \mathrm{~d} x=\)

  1. \(\frac{1}{2} \log \left|\frac{\cos x}{3 \sin x+4 \cos x}\right|+c\)
  2. \(\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c\)
  3. \(\frac{1}{3} \log \left|\frac{3 \cos x+\sin x}{3 \cos x+4 \sin x}\right|+c\)
  4. \(\frac{1}{2} \log \left|\frac{\cos x+4 \sin x}{3 \cos x+4 \sin x}\right|+c\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{1}{3} \log \left|\frac{\sin x}{3 \cos x+4 \sin x}\right|+c\)

Integration using Trigonometric Identities Question 3 Detailed Solution

Integration using Trigonometric Identities Question 4:

∫(tan7 x + tan x)dx =

  1. \(\frac{\tan ^2 x}{12}\left(2 \tan ^4 x-3 \tan ^2 x+6\right)+c\)
  2. \(\frac{\tan ^2 x}{6}-\frac{\tan ^5 x}{4}+\frac{\tan ^4 x}{2}+c\)
  3. \(\frac{\tan ^2 x}{6}\left(\tan ^4 x+3 \tan ^2 x+4\right)+c\)
  4. \(\frac{\tan x}{12}\left(\tan ^4 x-3 \tan ^2 x+6\right)+c\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{\tan ^2 x}{12}\left(2 \tan ^4 x-3 \tan ^2 x+6\right)+c\)

Integration using Trigonometric Identities Question 4 Detailed Solution

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