Leadership

Mathematics

Twelve Standard

Test your understanding of this lesson List of some frequently used formula in integration | Part-1:-

1)
\(\int g(x)dx=g(x)\), then \(\int g(x)[f(x)+f'(x)]dx\) is equal to
  • g(x)f(x)+g(x)f'(x)+c
  • g(x)f(x)-g(x)f'(x)+c
  • g(x)f'(x)+c
  • g(x)f(x)+c
2)
If I=\(\int |x|dx,\) then I is equal to
  • \(\frac{x^{2}}{2}+c\)
  • -\(\frac{x^{2}}{2}+c\)
  • \(\frac{|x|^{2}}{2}+c\)
  • \(\frac{x|x|}{2}+c\)
3)
If \(\int g(x)dx=g(x)\), then \(\int f(x)g(x)[f(x)+2f'(x)]dx\) is equal to
  • f(x)g(x)+c
  • \(f^{2}(x)g(x)+c\)
  • [f(x)-f'(x)]g(x)+c
  • \(f^{2}(x)g'(x)+c\)
4)
\(\int (1+2^{x}\log_{e}{2})dx=f(x)\), and f(2)=0, then f(x) is
  • \(x+2^{x}\)
  • \(x+2^{x}+4\)
  • \(x+2^{x}-6\)
  • None of these
5)
The value of \(\frac{\text{d}}{\text{d}x}\Big(\int f(x)dx\Big)\) is equal to
  • f(x)f'(x)
  • \(\frac{[f'(x)]^{2}}{2}\)
  • f(x)
  • None of these
Hand draw

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