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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
If $\int {f(x)\,dx = f(x)} ,$ then ${\int {\left[ {f(x)} \right]} ^2}\,\,dx$ is
  • ✓
    $\frac{1}{2}{\left[ {f\left( x \right)} \right]^2}$
  • B
    ${\left[ {f\left( x \right)} \right]^3}$
  • C
    $\frac{{{{\left[ {f\left( x \right)} \right]}^3}}}{3}$
  • D
    ${\left[ {\,f\left( x \right)} \right]^2}$
✓

Answer

Correct option: A.
$\frac{1}{2}{\left[ {f\left( x \right)} \right]^2}$
a
(a) Trick : Let $f(x) = {e^x},$ then$\int {f(x)dx = f(x)} $
$\therefore \,\int {{{({e^x})}^2}dx = \frac{{{e^{2x}}}}{2} = \frac{1}{2}{{[f(x)]}^2}.} $

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