Definite-Integration Question 536
Question: If $ f(t)=\int_{,-t}^{,t}{\frac{dx}{1+x^{2}},} $ then $ {f}’(1) $ is
[Roorkee 2000]
Options:
A) Zero
B) 2/3
C) $ -,1 $
D) 1
Show Answer
Answer:
Correct Answer: D
Solution:
Given $ f(t)=\int_{-t}^{t}{\frac{dx}{1+x^{2}}} $ $ =[{{\tan }^{-1}}x]_{-t}^{t} $ $ =2{{\tan }^{-1}}t $ Differentiating with respect to t, $ {f}’(t)=\frac{2}{1+t^{2}} $
Þ $ f’(1)=\frac{2}{2}=1 $ .
BETA
