Kc Sinha Mathematics Class 12 Solutions Pdf Fixed Apr 2026

"Use by parts. Ans: (x²/2) sin⁻¹ x + ..." (cut off)

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. Kc Sinha Mathematics Class 12 Solutions Pdf Fixed

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. "Use by parts

Integrate ∫ x sin⁻¹ x dx

Published by: Academic Help Desk Reading Time: 4 minutes No – for concept building