Questions and Solutions

Class: 12 Subject: Math Type: Mcq Year: 2022

Question 1:

If \(\int x^3f(x)\,dx = x^4f(x) - \int x^4f'(x)\,dx\), then \(f(x)\) is:

  • A. \(\log x\)
  • B. \(e^x\)
  • C. \(x\)
  • D. \(\sin x\)
Class: 12 Subject: Math Type: Mcq Year: 2022

Question 2:

If \(\int \frac{f'(x)}{f(x)}\,dx = \log |f(x)| + C\), then \(\int \frac{2x}{x^2 + 1}\,dx\) equals:

  • A. \(\log |x^2+1| + C\)
  • B. \(\log(x^2+1) + C\)
  • C. \(\tan^{-1}(x) + C\)
  • D. \(\frac{1}{x^2+1} + C\)