Question

Ques.
Integrate the following ​

Answer 1

Answer:

given to integrate ₀∫ⁿ´⁴ (1 - cos 2x ) dx

₀∫ⁿ´⁴(1 - 2cos²x - 1)¹´²dx [ cos 2x = 2cos²x -1]

=> ₀∫ⁿ´⁴ √(2 cos²x) dx [ a¹´² = √a ]

=> ₀∫ⁿ´⁴ √2 cos x dx

=> √2 [ sin x]ⁿ´⁴₀

=> √2 [ sin π/4 - sin 0 ]

=> √2 [ 1/√2 - 0 ]

=> √2 × 1/√2

=> 1