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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
If $\frac{\text{dy}}{\text{dx}}=\cos(2\text{x})$ then $y =$
  • ✓
    $\frac{\sin(2\text{x)}}{\text{2}}+\text{c}$
  • B
    $2\sin(2\text{x})+\text{c}$
  • C
    $\frac{\sin(\text{x})}{2}+\text{c}$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{\sin(2\text{x)}}{\text{2}}+\text{c}$
Using substitution method.
$u = 2x$
$du = 2dx$
$\frac{\text{du}}{2}=\text{dx}$
Plug in.
$\text{dy}=\frac{1}{2}\cos(\text{u})\text{du}$
Integrate.
$\text{y}=\frac{\sin(2\text{x})}{2}+\text{c}$

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