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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{{{\sin }^3}x + {{\cos }^3}x}}{{{{\sin }^2}x{{\cos }^2}x}}} \;dx = $
  • A
    $\tan x + \cot x + c$
  • B
    $\tan x - \cot x + c$
  • C
    ${\rm{cosec}}\,x - \cot x + c$
  • ✓
    $\sec x - {\rm{cosec}}\,x + c$
✓

Answer

Correct option: D.
$\sec x - {\rm{cosec}}\,x + c$
d
(d) $\int_{}^{} {\frac{{{{\sin }^3}x + {{\cos }^3}x}}{{{{\sin }^2}x{{\cos }^2}x}}\,dx} = \int_{}^{} {\left( {\frac{{\sin x}}{{{{\cos }^2}x}} + \frac{{\cos x}}{{{{\sin }^2}x}}} \right)\,dx} $

$\int (sec x   tan x + cosec x   cot x)dx $

$ = \sec x - \cos {\rm{ec}}x + c$

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