Mathbee CBSE Mathbee · CBSE Class 12 Maths
NCERT Class 12 · Ch 7 Exercise 7.10 · Q21

NCERT Class 12 Maths · Chapter 7 Integrals · Exercise 7.10 Question 21

Evaluate \(\int\limits_{0}^{\frac{\pi}{2}} \log{\left(\frac{3 \sin{\left(x \right)} + 4}{3 \cos{\left(x \right)} + 4} \right)}\, dx\) using definite-integral properties.

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: C: \(0\)
  1. Reflect x↦π/2−x: the fraction becomes its reciprocal.
  2. The log changes sign, so I=−I and I=0. All logarithm arguments are positive.

Master Chapter 7: Integrals

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →
← Previous Question
Evaluate ∫₋π/₂^π/₂(x³+x cos x+tan⁵x+1)dx.

All Questions in Integrals — Exercise 7.10

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21

Related Questions in Integrals

Class 12 Integrals · Mcq Single Correct
Evaluate \(\int x^2e^{x^3}\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(1+x)\sec^2(xe^x)\,dx\) on an interval where defined.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(\cos x-\sin x)\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int dx/(\sin^2x\cos^2x)\) on an interval avoiding its poles.
Class 12 Integrals · Mcq Single Correct
If \(\int\frac{3e^x-5e^{-x}}{4e^x+5e^{-x}}dx=ax+b\ln|4e^x+5e^{-x}|+C\), find a,b.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).