Integral Calculus By Das And Mukherjee Pdf |best| May 2026

5️⃣ TRIG SUBSTITUTIONS • √(a²–x²) → x = a sinθ • √(a²+x²) → x = a tanθ • √(x²–a²) → x = a secθ • Remember dx and simplify.

7️⃣ QUICK CHECKLIST BEFORE FINISHING • Did I revert u→x (if indefinite)? • Did I adjust limits (if definite)? • Is the result simplified? (Combine logs, rationalize) • Add constant C for indefinite integrals. integral calculus by das and mukherjee pdf

------------------------------------------------- CHAPTER 3 – TECHNIQUES OF INTEGRATION ------------------------------------------------- 1️⃣ SUBSTITUTION • Look for f(g(x))·g'(x) pattern. • Set u = g(x) → du = g'(x)dx. • Replace limits if it’s a definite integral. 5️⃣ TRIG SUBSTITUTIONS • √(a²–x²) → x =

4️⃣ TRIG INTEGRALS • Powers of sin/cos: - If odd power of sin → u = cos. - If odd power of cos → u = sin. • Both even → use identities: sin²x = (1‑cos2x)/2, cos²x = (1+cos2x)/2 • Products sin·cos → use substitution u = sin or cos. • Is the result simplified