SHIVAM PRADHAN
Articles by SHIVAM PRADHAN
Area Under Curves and Area Between Curves | NIMCET
Learn how to find the area under a curve, area with respect to the y-axis, area between two curves, and standard areas of the circle, ellipse and parabola regions, for NIMCET.
4 min read
Definite Integrals of Even and Odd Functions | NIMCET
Learn how even and odd functions simplify definite integrals over symmetric limits, how to integrate periodic functions, and the Leibniz rule for differentiating integrals, with a NIMCET syllabus note.
4 min read
Definite Integrals: Properties and King's Property | NIMCET
Learn the fundamental theorem of calculus, evaluating definite integrals, substitution with limits, and the key properties including King's property and splitting the interval, for NIMCET.
4 min read
Integration by Parts and Partial Fractions | NIMCET
Learn integration by parts with the ILATE rule, the eˣ[f(x) + f′(x)] shortcut, partial fractions for rational functions, and the special integrals of 1/(x² ± a²) and 1/√(a² − x²), for NIMCET.
4 min read
Indefinite Integrals: Formulas and Substitution | NIMCET
Learn integration as the reverse of differentiation, the standard integral formulas, integration by substitution, trigonometric identities in integration, and the f′(x)/f(x) shortcut, for NIMCET.
3 min read
Monotonicity, Maxima and Minima of Functions | NIMCET
Learn increasing and decreasing functions, critical points, the first and second derivative tests, absolute maxima and minima on closed intervals, and optimisation word problems, for NIMCET.
5 min read
Applications of Derivatives: Tangents and Normals | NIMCET
Learn derivatives as rates of change, related rates, equations of tangents and normals, angle between curves, lengths of tangent and normal, and approximations using differentials, for NIMCET.
4 min read
Higher Derivatives, Rolle's Theorem and MVT | NIMCET
Learn second and higher-order derivatives, nth derivatives of standard functions, and Rolle's theorem and Lagrange's mean value theorem with their conditions and applications, for NIMCET.
4 min read
Chain Rule, Implicit and Parametric Differentiation | NIMCET
Learn standard derivatives, product, quotient and chain rules, implicit, parametric and logarithmic differentiation, and derivatives of inverse trig functions with substitution, for NIMCET.
4 min read
Differentiability: Left and Right Hand Derivatives | NIMCET
Learn the derivative from first principles, left-hand and right-hand derivatives, the link between differentiability and continuity, and how to test |x|, [x] and piecewise functions, for NIMCET.
4 min read
Continuity of Functions and Types of Discontinuity | NIMCET
Learn the definition of continuity at a point and on an interval, removable, jump and infinite discontinuities, continuity of standard and combined functions, and the intermediate value theorem.
4 min read
One-Sided Limits and Limits at Infinity | NIMCET
Learn left-hand and right-hand limits, when a limit exists, limits at infinity for rational functions, limits of greatest integer and modulus functions, and the sandwich theorem, for NIMCET.
4 min read