Definite Integration Question 286
Question: $ \int _{\pi /4}^{\pi /2}{\cos \theta cose{c^{2}}\theta d\theta =} $
[Roorkee 1978]
Options:
A) $ \sqrt{2}-1 $
B) $ 1-\sqrt{2} $
C) $ \sqrt{2}+1 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ \int _{\pi /4}^{\pi /2}{\cos \theta \frac{1}{{{\sin }^{2}}\theta }d\theta } $
Put $ t=\sin \theta \Rightarrow dt=\cos \theta d\theta , $ then we have $ \int _{1/\sqrt{2}}^{1}{\frac{1}{t^{2}}dt}=[ \frac{-1}{t} ] _{1/\sqrt{2}}^{1}=\sqrt{2}-1 $ .
BETA
