Integral Calculus By Das And Mukherjee Pdf May 2026

------------------------------------------------- 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 = a sinθ • √(a²+x²) → x = a tanθ • √(x²–a²) → x = a secθ • Remember dx and simplify. integral calculus by das and mukherjee pdf

2️⃣ INTEGRATION BY PARTS • Formula: ∫u dv = uv – ∫v du • Choose u = “algebraic” (poly, log) → du simpler. • dv = “trig, exp, power” → v easy. 5️⃣ TRIG SUBSTITUTIONS • √(a²–x²) → x =

------------------------------------------------- Print and stick it on the inside cover of your notebook. Use it as a first‑pass reference each time you start a new problem. | Week | Focus | Goal (hours) | Sample Problems | |------|-------|--------------|-----------------| | 1 | Definite integrals & basic techniques | 8–10 hrs | Compute area between curves, evaluate ∫₀^π/2 sin²x dx, ∫₁^4 (x³‑2x)dx | | 2 | Advanced techniques (partial fractions, trig subs) | 10–12 hrs | ∫(2x+3)/(x²‑x‑6)dx, ∫dx/√(9‑x²), ∫tan³x sec²x dx | | 3 | Applications (volumes, arc length, work) | 12 hrs | Volume of solid generated by rotating y = √x about x‑axis, surface area of y = ln x, work done pulling a rope | | 4 | Improper integrals & ODEs | 10 hrs | Test convergence of ∫₁^∞ 1/(x ln²x)dx, solve dy/dx = y·tan x, find particular solution with y(0)=2 | evaluate ∫₀^π/2 sin²x dx