Definite Integration Question 472
Question: $ \int_0^{2/3}{\frac{dx}{4+9x^{2}}=} $
[MP PET 1997]
Options:
A) $ \frac{\pi }{12} $
B) $ \frac{\pi }{24} $
C) $ \frac{\pi }{4} $
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_0^{2/3}{\frac{dx}{4+9x^{2}}=\frac{1}{9}\int_0^{2/3}{\frac{dx}{{{(2/3)}^{2}}+x^{2}}}} $
$ =\frac{1}{9}\times \frac{1}{2/3}( {{\tan }^{-1}}\frac{x}{2/3} )_0^{2/3}=\frac{\pi }{4}\times \frac{1}{6}=\frac{\pi }{24} $ .
BETA
