DEFINITE INTEGRALS

Definition of Definite Integrals: Example  : Soln: Example  : Soln: Example  : Soln: Example  : Soln: Example  : Soln: Example  : Soln: Example  : Soln: Example  : Soln: Example  : Soln: du  = cos x dx Example  : Soln: Adding ( 1 ) &  ( 2 )

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BERNOULLLI’S FORMULA

If u and v are functions x, then Bernoulli’s form of integration by parts formula is Where u΄, u΄΄,u΄΄΄….. are successive differentiation of the function u and v, v1, v2, v3, …………. the successive integration of the function dv. Note: The function ‘u’ is differentiated up to constant. Example  : Soln: ILATE Example  : Soln: Example  : Soln: ILATE Example  : Soln: ILATE Example  : Soln: ILATE

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5.1 INTEGRATION BY PARTS

Introduction: When the integrand is a product of two functions and the method of decomposition or substitution can not be applied, then the method of by parts is used. Integraiton by parts formula: The above formula is used by taking proper choice of ‘u’ and ‘dv’. ‘u’ should be chosen based on thefollowing order of Preference. Simply remember ILATE 1. Inverse trigonometric functions: 2. Logarithmic functions: log x 3. Algebraic functions: 4. Trigonometric functions: sin x, cos x, tan x, etc. 5. Exponential functions: Example:  Soln: ILATE u = x                                    …

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