Get Answers to all your Questions

header-bg qa

Provide solution for RD Sharma maths class12 Chapter Definite Integrals exercise 19.2 question 14.

Answers (1)

Answer: \frac{1}{4}\log \left ( \frac{3+2\sqrt{3}}{3} \right )

Hint: We use indefinite integral formula then put limits to solve this integral.

Given: \int_{0}^{\frac{\pi}{3}}\frac{\cos x }{3+4 \sin x}dx

Solution: I=\int_{0}^{\frac{\pi}{3}}\frac{\cos x }{3+4 \sin x}dx

Put 3+4\sin x=t

4\cos x \; dx=dt

\cos x\; \; dx=\frac{dt}{4}

When x=0  then t=3  and

when x=\frac{\pi}{3}  then t=3+2\sqrt{3}

\begin{aligned} &I=\int_{3}^{3+2 \sqrt{3}} \frac{1}{t} \frac{d t}{4} \\ &I=\frac{1}{4} \int_{3}^{3+2 \sqrt{3}} \frac{1}{t} d t \\ &=\frac{1}{4}[\log |t|]_{3}^{3+2 \sqrt{3}} \\ &=\frac{1}{4}[\log (3+2 \sqrt{3})-\log 3] \\ &=\frac{1}{4} \log \left(\frac{3+2 \sqrt{3}}{3}\right) \end{aligned}



Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support