Calculus forms the backbone of NEB Class 12 Mathematics, comprising over 30 marks across indefinite integrals, definite integrals, and differential equations.
1. Integration by Parts with ILATE
Inverse, Logarithmic, Algebraic, Trigonometric, Exponential. When integrating functions like $x e^x$ or $x \ln x$, choosing $u$ and $v$ according to ILATE prevents infinite recursive loops.
2. First-Order Linear Differential Equations
Equations of the form $\frac{dy}{dx} + P(x)y = Q(x)$ require finding the Integrating Factor: $I.F. = e^{\int P(x) dx}$. The general solution is simply $y \cdot (I.F.) = \int [Q(x) \cdot (I.F.)] dx + C$. Practice this sequence until it becomes automatic.
