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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {2x{{\cos }^3}{x^2}\sin {x^2}dx = } $
  • ✓
    $ - \frac{1}{4}{\cos ^4}{x^2} + c$
  • B
    $\frac{1}{4}{\cos ^4}{x^2} + c$
  • C
    ${\cos ^4}{x^2} + c$
  • D
    None of these
✓

Answer

Correct option: A.
$ - \frac{1}{4}{\cos ^4}{x^2} + c$
a
(a) Put $t = \cos {x^2} \Rightarrow dt = - 2x\sin {x^2}dx,$ then
$\int_{}^{} {2x{{\cos }^3}{x^2}\sin {x^2}dx} = - \int_{}^{} {{t^3}dt} = - \frac{{{t^4}}}{4} + c$
$ = - \frac{1}{4}{\cos ^4}{x^2} + c.$

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