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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
Question
If $\frac{\text{dy}}{\text{dx}}=\cos(2\text{x})$ then y = 
  1. $\frac{\sin(2\text{x)}}{\text{2}}+\text{c}$
  2. $2\sin(2\text{x})+\text{c}$
  3. $\frac{\sin(\text{x})}{2}+\text{c}$
  4. None of these
✓

Answer

  1. $\frac{\sin(2\text{x)}}{\text{2}}+\text{c}$

Solution:

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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