Calculus is an integral part of mathematics. Based on the study of how things change, calculus allows students to identify the effects of changing conditions on the system. It covers various topics like derivatives, integrals, infinite series, limits, functions, etc. Calculus is primarily categorized into two important sections one is Differential Calculus and the other […]

# Calculus

# calculus worked examples

2. A population is distributed according to the four standard blood types as follows: A – 42 % O – 33 % B – 18 % AB – 7 % (a) Assuming that people choose their mates independent of blood type, find the probability that a random sampled couple from this population will have the […]

# Calculus convergence example problem

1. Show that the integral converges for all values of a < 0. ∞ ∫ e^ax cos x dx 0 Solution: ∞ t ∫ e^ax cos x dx = limit ∫ e^ax cos x dx 0 t->∞ 0 t = limit ∫ e^ax d (sinx) t->∞ 0 Applying integration by parts, ∫e^ax cosx dx = […]

# Integration of tan^3sec^4x dx

Integration of tan^3sec^4x dx a calculus question by @tutorvista Substitution Method Here the trick is :: write sec^4 x as sec^2 x times sec^2 x integration of tan^3x sec^4x dx = now take the tanx as a new parameter u then du = sec^2 dx so we shall plug in terms of u integration […]