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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
The value of $\int {{e^{2x}}(2\sin 3x + 3\cos 3x)\,\,dx} $ is
  • ✓
    ${e^{2x}}\sin 3x$
  • B
    ${e^{2x}}\cos 3x$
  • C
    ${e^{2x}}$
  • D
    ${e^{2x}}(2\sin 3x)$
✓

Answer

Correct option: A.
${e^{2x}}\sin 3x$
a
(a) $\int {{e^{2x}}(2\sin 3x + 3\cos 3x)\,\,dx} $
$ = {e^{2x}}\sin 3x + c$.$\left\{ {\because \int {{e^{mx}}[mf(x) + f'(x)]\,dx = {e^{mx}}f(x) + c} } \right\}$

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