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INTEGRALS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINTEGRALS1 Mark
Question
$\int\frac{\sin^6\text{x}}{\cos^8\text{x}}\text{ dx}=$
  1. $\tan7\text{x}+\text{C}$
  2. $\frac{\tan^7\text{x}}{7}+\text{C}$
  3. $\frac{\tan7\text{x}}{7}+\text{C}$
  4. $\sec^7\text{x}+\text{C}$
✓

Answer

  1. $\frac{\tan^7\text{x}}{7}+\text{C}$
Solution:
$\text{I}=\int\frac{\sin^6\text{x dx}}{\cos^8\text{x}}$
$\text{I}=\int\tan^6\text{x}\sec^2\text{x dx}$
Put $\tan\text{x}=\text{t}$
$\sec^2\text{x dx}=\text{dt}$
$\text{I}=\int\text{t}^6\text{dt}$
$\text{I}=\frac{\text{t}^7}{7}+\text{C}$
$\text{I}=\frac{\tan^7\text{x}}{7}+\text{C}$

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