Given below are two statements. Statement - 1: If f(x)= _ 1 ^ x _ r t 1+t+t^ 2 d t then…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Given below are two statements.
Statement - 1: If \(f(x)=\int_{1}^{x} \frac{\log _{\mathbf{r}} t}{1+t+t^{2}} d t\) then \(f(x)=f\left(\frac{1}{x}\right)\) for all x > 0.
Statement - 2: If \(f(x)=\int_{1}^{x} \frac{\log _{\mathbf{r}} t}{1+t} d t_{1} \text { then } f(x)+f\left(\frac{1}{x}\right)=\frac{\left[\log _{\mathbf{r}} x\right]^{2}}{2}\).
In the light of the above statements, choose the correct answer from the options given below:
- Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both Statements are true but Statement - 2 is not a correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(D) Statement - 1 is false and Statement - 2 is true
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