Integral Calculus Question 50
Question: $ \int_{{}}^{{}}{\frac{x\ dx}{(x^{2}-a^{2})(x^{2}-b^{2})}=} $
[Roorkee 1976]
Options:
A) $ \frac{1}{a^{2}-b^{2}}\log ( \frac{x^{2}-a^{2}}{x^{2}-b^{2}} )+c $
B) $ \frac{1}{a^{2}-b^{2}}\log ( \frac{x^{2}-b^{2}}{x^{2}-a^{2}} )+c $
C) $ \frac{1}{2(a^{2}-b^{2})}\log ( \frac{x^{2}-a^{2}}{x^{2}-b^{2}} )+c $
D) $ \frac{1}{2(a^{2}-b^{2})}\log ( \frac{x^{2}-b^{2}}{x^{2}-a^{2}} )+c $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{\frac{x}{(x^{2}-a^{2})(x^{2}-b^{2})}},dx $ $ =\frac{1}{a^{2}-b^{2}}[ \int_{{}}^{{}}{\frac{x}{x^{2}-a^{2}},dx-\int_{{}}^{{}}{\frac{x,dx}{x^{2}-b^{2}}}} ] $ .
BETA
