It is a legendary book for mastering calculus, algebra, and vectors. However, there is a massive problem students face online:
If you are a Class 12 student preparing for your Board Exams (especially CBSE, Bihar Board, or UP Board), you have almost certainly heard of—or struggled with— book.
Integrate ∫ x sin⁻¹ x dx
After searching through 20+ websites and Telegram channels, I have finally found a version of the KC Sinha Mathematics Class 12 Solutions PDF.
| Volume | Chapter No. | Topic | |--------|-------------|-------| | 1 | 1 | Relations and Functions | | 1 | 2 | Inverse Trigonometric Functions | | 1 | 3 | Matrices | | 1 | 4 | Determinants | | 1 | 5 | Continuity and Differentiability | | 1 | 6 | Differentiation (Advanced) | | 2 | 7 | Applications of Derivatives (AOD) | | 2 | 8 | Indefinite Integration | | 2 | 9 | Definite Integration | | 2 | 10 | Differential Equations | | 2 | 11 | Vector Algebra | | 2 | 12 | 3D Geometry | | 2 | 13 | Linear Programming | | 2 | 14 | Probability | Important Note: I do not host pirated content. KC Sinha books are available legally. However, many schools provide a "question bank" or "solution set" for students. Kc Sinha Mathematics Class 12 Solutions Pdf Fixed
Published by: Academic Help Desk Reading Time: 4 minutes
"Use by parts. Ans: (x²/2) sin⁻¹ x + ..." (cut off) It is a legendary book for mastering calculus,
Let I = ∫ x sin⁻¹ x dx Put sin⁻¹ x = t → x = sin t, dx = cos t dt I = ∫ sin t . t . cos t dt = (1/2) ∫ t sin 2t dt Apply integration by parts: = (1/2)[ t (-cos 2t)/2 - ∫ (-cos 2t)/2 dt ] = - (t cos 2t)/4 + (1/8) sin 2t + C Back substitute: t = sin⁻¹ x, sin 2t = 2x√(1-x²), cos 2t = 1-2x² Final answer: (1/4)(2x²-1) sin⁻¹ x + (x/4)√(1-x²) + C Crystal clear, no missing steps. Yes – for solving doubts. No – for concept building.
