If ∫π30cos4xdx=aπ+b3√, where a and b are rational numbers, then 9a+8b is equal to :

Question

If ∫π30cos4xdx=aπ+b3√, where a and b are rational numbers, then 9a+8b is equal to :
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Solution 1

To solve this problem, we need to use the power-reduction identity for cosine, which is cos^2(x) = (1 + cos(2x))/2.

Step 1: Rewrite cos^4(x) as (cos^2(x))^2.

Step 2: Substitute the power-reduction identity into the integral: ∫π/3 0 (1 + cos(2x))^2 dx.

Step 3: Expand the square: ∫π/3 0 (1 + 2cos( Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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