JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int_0^{\frac{\pi}{3}} \cos ^4 x d x=a \pi+b \sqrt{3}\), where \(a\) and \(b\) are rational numbers, then \(9 a+8 b\) is equal to :
- A \(2\)
- B \(1\)
- C \(3\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\( \int_0^{\pi / 3} \cos ^4 x d x \) \( =\int_0^{\pi / 3}\left(\frac{1+\cos 2 x}{2}\right)^2 d x \) \( =\frac{1}{4} \int_0^{\pi / 3}\left(1+2 \cos 2 x+\cos ^2 2 x\right) d x \)…
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