DEFINITE INTEGRALS (Excercise Problems)
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N-Unit – IV – INTEGRAL CALCULUS – II
DEFINITE INTEGRALS
Definition of Definite Integrals: Example 1: Example 2: Example 4: Example 5: Example 6: Example 7: Example 8: Example 9: Example 10: Example 11: Example 12: Example 13: du = cos x dx Example 14: Adding ( 1 ) & ( 2 )
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BERNOULLI’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 1: Example 2: Example 3: Example
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4.1 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
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