What Is the Integral of cos²x?
Updated: Sep 13
At first glance, this might seem tricky because cos²x is not a simple function to integrate directly. Unlike basic trigonometric functions such as sin(x) or cos(x), squaring the cosine function changes its behavior and complicates the integration process.
Final Result: (Watch Full Video Solution below or Scroll for Step by Step Solution!)
The key to solving this integral lies in using trigonometric identities to simplify the expression before integrating.
Full Video Explanation
Watch how the integral of cos²x is solved quickly using the power-reduction identity.
Step by Step Solution:
Step 1: Apply Power Reduction Identity shown below:
This formula transforms the square of cosine into a sum of simpler cosine terms, making integration straightforward.
Step 2: Substitute result from step 1 in the Integral:
Step 3: Split the Integral:
Step 4: Integrate each term to get final result
Tips for Integrating Other Powers of Cosine
The approach used for cos²x can extend to other powers of cosine, though the process may become more complex.
For even powers, use power-reduction formulas repeatedly.
For odd powers, separate one cosine factor and convert the rest using identities.
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