Test Index

NCERT Class XII Mathematics Chapter - - Solutions

Show Para  Hide Para 
Exercise - 7.9
Evaluate the definite integrals in Exercises 176 to 195.
© examsnet.com
Question : 183 of 271
Marks: +1, -0
∫π6π4csc⁡x dx\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} \csc x \, dx
Solution:  
∫π6π4csc⁡x dx\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} \csc x \, dx
=[log⁡(csc⁡x−cot⁡x)]π6π4= \left[ \log(\csc x - \cot x) \right]_{\frac{\pi}{6}}^{\frac{\pi}{4}}
=log⁡(csc⁡π4−cot⁡π4)−log⁡(csc⁡π6−cot⁡π6)= \log\left(\csc \frac{\pi}{4} - \cot \frac{\pi}{4}\right) - \log\left(\csc \frac{\pi}{6} - \cot \frac{\pi}{6}\right)
=log⁡(2−1)−log⁡(2−3)= \log(\sqrt{2} - 1) - \log(2 - \sqrt{3})
=log⁡(2−12−3)= \log\left(\frac{\sqrt{2} - 1}{2 - \sqrt{3}}\right)
© examsnet.com
Go to Question:
Prev Question
Next Question
Advertisements