WBJEE · Maths · Definite Integration
If \(\mathrm{I}_1=\int_0^{3 \pi} \mathrm{f}\left(\cos ^2 \mathrm{x}\right) \mathrm{dx}\) and \(\mathrm{I}_2=\int_0^\pi \mathrm{f}\left(\cos ^2 \mathrm{x}\right) \mathrm{dx}\), then
- A \(\mathrm{I}_1=\mathrm{I}_2\)
- B \(3 \mathrm{I}_1=\mathrm{I}_2\)
- C \(\mathrm{I}_1=3 \mathrm{I}_2\)
- D \(\mathrm{I}_1=5 \mathrm{I}_2\)
Answer & Solution
Correct Answer
(C) \(\mathrm{I}_1=3 \mathrm{I}_2\)
Step-by-step Solution
Detailed explanation
Hints : \(I_1=3 \int_0^\pi \mathrm{f}\left(\cos ^2 x\right) d x=3 I \quad\) [period is \(\pi\) ]
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