Here you will learn integration of trigonometric function with examples. Let’s begin – Integration of Trigonometric Function (i) \(\int\) \(sin^mxcos^nx\) Case-1 : When both m & n \(\in\) natural numbers. (a) If one of them is odd, then substitute for the term of even power. (b) If both are odd, substitute either of them. (c) …
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Here you will learn Integration integration formulas for class 12. Let’s begin – Integration Formula for Class 12 (i) \(\int\) \({(ax+b)}^n\) dx = \({(ax+b)}^{n+1}\over {a(n+1)}\) + C ; n \(\ne\) -1 (ii) \(\int\) \(dx\over {ax+b}\) dx = \(1\over a\) ln|ax+b| + C (iii) \(\int\) \(e^{ax+b}\) dx = \({1\over {a}}e^{ax+b}\) + C or \(\int\) \(e^x\) = …
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Here you will learn how to solve mean by using step deviation method and by short method and properties of mean. Let’s begin – Mean By Short Method If the value of \(x_i\) are large, then calculation of A.M. by using mean formula is quite tedious and time consuming. In such case we take deviation …
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Here you will learn algebraic operations on functions, equal or identical functions and homogeneous function. Let’s begin – Algebraic Operations on Functions Various operations, namely addition, subtraction, multiplication, division etc on real function are : (i) Addition : Let f : \(D_1\) \(\rightarrow\) R and g : \(D_2\) \(\rightarrow\) R be two real functions. Then, …
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Here you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range. Let’s begin – Types of Functions in Maths (a) Polynomial function If a function is defined by f(x) = \(a_0x^n\) + \(a_1x^{n-1}\) + \(a_2x^{n-2}\) + ….. + \(a_{n-1}x\) + \(a_n\) where n is a non …
Here you will learn formula permutation and combination and properties of permutation and combination with examples. Let’s begin – Permutation and Combination Formula Permutation Each of the arrangements in a definite order which can be made by taking some or all of the things at a time is called a PERMUTATION. In permutation, order of …
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Here you will learn addition principle of counting and multiplication principle in permutation and combination with example. Let’s begin – If an event A can occur in ‘m’ different ways and another event B can occur in ‘n’ different ways, then the total number of different ways of- Multiplication Principle of Counting Simultaneous occurrences of …
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Here you will learn what is inverse relation, identity relation and posets in relation with example. Let’s begin – Definition of Inverse Relation If relation R is defined from A to B, then inverse relation would be defined form B to A, i.e. R : A \(\rightarrow\) B \(\implies\) aRb where a \(\in\) A, b …
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Here you will learn what is cartesian product of sets and what is relation and inverse relation with example. Let’s begin – Cartesian Product of Sets The cartesian product of two sets A, B is a non-void set of all ordered pair (a,b), where a \(\in\) A and b \(\in\) B. This is denoted by …
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Here you will learn what are the properties of logarithms and fundamental identities of logarithm with examples. Let’s begin – Every positive real number N can be expressed in exponential form as \(a^x\) = N where ‘a’ is also a positive real number different than unity and is called the base and ‘x’ is called …
