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Evaluate using Substitution MCQ Quiz in తెలుగు - Objective Question with Answer for Evaluate using Substitution - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Last updated on Apr 30, 2025

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

Latest Evaluate using Substitution MCQ Objective Questions

Evaluate using Substitution Question 1:

\(\displaystyle\int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x=\)

  1. \(-\frac{\pi}{2} \log 2\)
  2. \(-\frac{\pi}{8} \log 2\)
  3. \(-\frac{\pi}{14} \log 2\)
  4. \({-\frac{\pi}{28}} \log 2\)

Answer (Detailed Solution Below)

Option 2 : \(-\frac{\pi}{8} \log 2\)

Evaluate using Substitution Question 1 Detailed Solution

Evaluate using Substitution Question 2:

\(\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=\)

  1. \(\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)
  2. \({-\frac{4}{5}} \log |\cos 3 x+2 \sin 3 x|+\frac{7 x}{5}+\mathrm{c}\)
  3. \(\frac{7}{5} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+\mathrm{c}\)
  4. \(-\frac{8}{15} \log |\cos 3 x+2 \sin 3 x|+\frac{x}{5}+\mathrm{c}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)

Evaluate using Substitution Question 2 Detailed Solution

Evaluate using Substitution Question 3:

\(\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=\)

  1. \(\frac{1}{25} \operatorname{Tan}^{-1}\left(\frac{3}{4} \sec ^2 2 x\right)+\mathrm{c}\)
  2. \(\frac{1}{25} \operatorname{Tan}^{-1}\left(\frac{4}{3} \sec ^2 2 x\right)+\mathrm{c}\)
  3. \(\frac{1}{24} \operatorname{Tan}^{-1}\left(\frac{3}{4} \tan 2 x\right)+\mathrm{c}\)
  4. \(\frac{1}{24} \operatorname{Tan}^{-1}\left(\frac{4}{3} \tan 2 x\right)+\mathrm{c}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{1}{24} \operatorname{Tan}^{-1}\left(\frac{4}{3} \tan 2 x\right)+\mathrm{c}\)

Evaluate using Substitution Question 3 Detailed Solution

Top Evaluate using Substitution MCQ Objective Questions

Evaluate using Substitution Question 4:

\(\displaystyle\int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x=\)

  1. \(-\frac{\pi}{2} \log 2\)
  2. \(-\frac{\pi}{8} \log 2\)
  3. \(-\frac{\pi}{14} \log 2\)
  4. \({-\frac{\pi}{28}} \log 2\)

Answer (Detailed Solution Below)

Option 2 : \(-\frac{\pi}{8} \log 2\)

Evaluate using Substitution Question 4 Detailed Solution

Evaluate using Substitution Question 5:

\(\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=\)

  1. \(\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)
  2. \({-\frac{4}{5}} \log |\cos 3 x+2 \sin 3 x|+\frac{7 x}{5}+\mathrm{c}\)
  3. \(\frac{7}{5} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+\mathrm{c}\)
  4. \(-\frac{8}{15} \log |\cos 3 x+2 \sin 3 x|+\frac{x}{5}+\mathrm{c}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{7}{15} \log |\cos 3 x+2 \sin 3 x|-\frac{4}{5} x+c\)

Evaluate using Substitution Question 5 Detailed Solution

Evaluate using Substitution Question 6:

\(\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=\)

  1. \(\frac{1}{25} \operatorname{Tan}^{-1}\left(\frac{3}{4} \sec ^2 2 x\right)+\mathrm{c}\)
  2. \(\frac{1}{25} \operatorname{Tan}^{-1}\left(\frac{4}{3} \sec ^2 2 x\right)+\mathrm{c}\)
  3. \(\frac{1}{24} \operatorname{Tan}^{-1}\left(\frac{3}{4} \tan 2 x\right)+\mathrm{c}\)
  4. \(\frac{1}{24} \operatorname{Tan}^{-1}\left(\frac{4}{3} \tan 2 x\right)+\mathrm{c}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{1}{24} \operatorname{Tan}^{-1}\left(\frac{4}{3} \tan 2 x\right)+\mathrm{c}\)

Evaluate using Substitution Question 6 Detailed Solution

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