Suppose f, f prime and f prime prime are continuous on [0, e] and that f prime(e)=f(e)=f(1)=1 and ∫ limits1e (f(x)/x2) d x=(1/2), then the value of ∫ limits1e f prime prime(x) ln x d x equals -

Question

Suppose f, f prime and f prime prime are continuous on [0, e] and that f prime(e)=f(e)=f(1)=1 and ∫ limits1e (f(x)/x2) d x=(1/2), then the value of ∫ limits1e f prime prime(x) ln x d x equals - (A) 0 (B) 1 (C) 2 (D) none of these

Tardigrade Admin · Accepted Answer

Correct answer is (d) none of these

Q. Suppose f,f′ and f′′ are continuous on [0,e] and that f′(e)=f(e)=f(1)=1 and 1∫e​x2f(x)​dx=21​, then the value of 1∫e​f′′(x)lnxdx equals -

0

1

2

none of these

Correct answer is (d) none of these

Q. Suppose $f, f^{'}$ and $f^{''}$ are continuous on $[0, e]$ and that $f^{'} (e) = f (e) = f (1) = 1$ and $1 \int e \frac{f ( x )}{x ^{2}} d x = \frac{1}{2}$ , then the value of $1 \int e f^{''} (x) ln x d x$ equals -