If ∫ (x2-1/x3 √3 x4+2 x2-1) d x=f(x)+C, where f(1)=-1, then |f(-1)| is equal to

Question

If ∫ (x2-1/x3 √3 x4+2 x2-1) d x=f(x)+C, where f(1)=-1, then |f(-1)| is equal to (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

∫ (x-3-x-5/√3+2 x-2-x-4) d x 3+2 x-2-x-4=t2 (-4 x-3+4 x-5) d x=2 t d t ( x -3- x -5) dx =-(1/2) tdt ∴ I=∫ (-(1/2) t d t/t)=-(1/2) t+C=-(1/2) √3+2 x-2-x-4+C f(x)=-(1/2) √3+2 x-2-x-4 f(-1)=-(1/2) √3+2-1=-1 ⇒ | f (-1)|=1

Q. If ∫x33x4+2x2−1​x2−1​dx=f(x)+C, where f(1)=−1, then ∣f(−1)∣ is equal to

1

2

3

4

∫3+2x−2−x−4​x−3−x−5​dx 3+2x−2−x−4=t2 (−4x−3+4x−5)dx=2tdt (x−3−x−5)dx=−21​tdt ∴I=∫t−21​tdt​=−21​t+C=−21​3+2x−2−x−4​+C f(x)=−21​3+2x−2−x−4​ f(−1)=−21​3+2−1​=−1 ⇒∣f(−1)∣=1

Q. If $\int \frac{x ^{2} - 1}{x ^{3} 3 x ^{4} + 2 x ^{2} - 1} d x = f (x) + C$ , where $f (1) = - 1$ , then $∣ f (- 1) ∣$ is equal to