GATE | GATE-CS-2015 (Set 3) | Question 55
(A) A
(B) B
(C) C
(D) D
Answer: (A)
Explanation: Given-
Putting 
we get-
Subtracting the second equation from the first one we get-
Putting this value back in the first equation-
Now that we have 
we can find 
![\begin{flalign*} \int f(x)\:dx &= \int \frac{1}{(a^2-b^2)} \Big( b(\frac{1}{x}-x) + \frac{a-b}{x} - 25(a-b)\Big)\:dx \\ &= \frac{1}{(a^2-b^2)} \Big( b(\ln{x}-\frac{x^2}{2}) + (a-b)\ln{x} - 25(a-b)x\Big) \\ &= \frac{1}{(a^2-b^2)} \Big( \frac{-bx^2}{2} + a\ln{x} - 25(a-b)x\Big) \\ &\text{Putting the limits}\\ &= \frac{1}{(a^2-b^2)} \Big[ \frac{-bx^2}{2} + a\ln{x} - 25(a-b)x\Big] \limits_{1}^{2} \\ &= \frac{1}{(a^2-b^2)} \Big[ \big(-2b + a\ln{2} - 50(a-b)\big) - \big(-\frac{b}{2} + 0 - 25(a-b)\big) \Big] \\ &= \frac{1}{(a^2-b^2)} \Big( \frac{-3b}{2} + a\ln{2} - 25(a-b)\Big) \\ &= \frac{1}{(a^2-b^2)} \Big( \frac{47b}{2} + a(\ln{2} - 25)\Big) \\ \end{flalign*}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-ee416288ffe41af277877bf43b16dd32_l3.png "Rendered by QuickLaTeX.com")
Therefore the correct option is A.
Quiz of this Question
Please Login to comment...