Learn Basics and Advanced of definite and indefinite integration in calculus 2, practice differential and infinite sequences and series equations.
A definite integral has upper and lower limits on the integrals, the definite integral of f(x) between two limits a and b is the area under the curve from x=a to x=b. In this topic, we will learn to practice geometrical interpretation of definite integral where we will learn to solve approximate area under the graph and curve by integration, exact calculation of area by taking limits. Also practice on properties and application of definite integration and application of fundamental theorem of calculus.
The indefinite integral (or antiderivative) of f (x) is a function F(x) whose derivative is equal to f (x). This means that F ' (x) = f (x). In this topic, we will learn to practice on indefinite integration by substitution of trigonometric functions, integration of power of sin and cos functions and reduction formula, and tan and cot functions (other than sin and cos), also practice problems on advanced method of integration using partial fractions and calculus on exponential and log function.
A definite integral has upper and lower limits on the integrals, the definite integral of f(x) between two limits a and b is the area under the curve from x=a to x=b. In this topic, we will learn to practice problems on application of integration in geometry where we will learn to calculate arc length, area of surface of revolution and volume of solids-I and II. We will learn to practice on advanced method of definite integration by substitution, errors in approximate integration and tabular form and definition of improper integral and type 1 and 2. Also practice on probability on random and normal distribution and application of integration in economics and physics.
An equation that contains independent variable (usually ′x′) some functions of x, dependent variable (usually ′y′) some functions of y and at least one derivative term of y with respect to x is called a differential equation. In this topic, we will learn to practice on differential equations and their solutions and variable separation method. Also, learn to practice on rate of growth decay and further applications of differential equations.
Sequence is a list of number written in a definite order or having a particular pattern. If we add the terms of an infinite sequence we get an expression which is called an infinite series. In this topic, we will learn to practice problems on basics of sequence and series, different tests on series and P series, alternating series, ratio, root test and convergence interval. Also learn to practice problems on taylor, maclaurin, binomial power series and radius of convergence.