Secure 3 Marks Integration | CBSE Class 12

Welcome back to Mathematics Time! 🚀 In today's video, we are solving one of the most frequently asked integration questions in Class 12 board exams. If you want to secure those easy 3 marks, make sure you understand the trigonometric identities used in this solution!

Question Solved in this Video:
Evaluate the integral of (cos 2x - cos 2α) / (cos x - cos α) dx

Topics Covered:

Application of double angle formulas: cos 2x = 2cos²x - 1

Step-by-step simplification of trigonometric integrands

Indefinite integration techniques for board exams

Don't forget to pause the video and try to solve it yourself first!

This video from Mathematics Time provides a step-by-step solution to a frequently asked integration problem in Class 12 CBSE exams: Evaluate the integral of (cos 2x - cos 2α) / (cos x - cos α) dx.

Key Steps in the Solution:
Trigonometric Simplification (0:33 - 2:10): The video uses the double angle identity cos 2x = 2cos²x - 1 to rewrite both terms in the numerator, which helps simplify the expression and eliminate the constant terms.
Factorization (2:43 - 3:15): After simplifying, the numerator becomes a difference of squares (2cos²x - 2cos²α). Using the a² - b² = (a+b)(a-b) identity, the expression is factored to allow the cancellation of the denominator (cos x - cos α).
Integration (3:37 - 5:45): This is the most crucial part where students often make mistakes. The speaker emphasizes that since the integration is with respect to x, the cos α term is treated as a constant and moved outside the integral.
Final Result (5:45 - 5:57): By integrating cos x to get sin x and integrating the constant cos α with respect to x, the final solution is derived as 2 sin x + 2x cos α + C.

If you found this explanation helpful, please hit the LIKE button, share it with your friends, and SUBSCRIBE to Mathematics Time for more daily math solutions and exam tricks! 📚✏️

Drop a comment below if you have any questions or if there is a specific problem you want me to solve next!

#Integration #Class12Maths #CBSEBoardExams #MathematicsTime #MathTricks #Calculus

Видео Secure 3 Marks Integration | CBSE Class 12 канала Mathematics Time