If …, where … and … are rational numbers, then … is equal to :

Option A. To solve the given integral …, we'll apply a known power-reduction formula that allows us to express even powers of sine and cosine functions in terms of cosine of multiple angles. Specifically for …, we can write it in terms of double angles as:

Definite Integration

JEE Main 2024 · 1 Feb, Evening shift · Q3467

MathematicsHard210×since 2002Q3467

\int\limits_0^{\frac{\pi}{3}} \cos ^4 x \mathrm{~d} x=\mathrm{a} \pi+\mathrm{b} \sqrt{3}

, where

\mathrm{a}

and

\mathrm{b}

are rational numbers, then

9 \mathrm{a}+8 \mathrm{b}

is equal to :

Definite Integration

JEE Main 2024 · 1 Feb, Evening shift · Q3467

MathematicsHard210×since 2002Q3467

\int\limits_0^{\frac{\pi}{3}} \cos ^4 x \mathrm{~d} x=\mathrm{a} \pi+\mathrm{b} \sqrt{3}

, where

\mathrm{a}

and

\mathrm{b}

are rational numbers, then

9 \mathrm{a}+8 \mathrm{b}

is equal to :

Definite Integration

More on Definite Integration

Definite Integration

More on Definite Integration