Integration-mathematics, Mathematics


Integration is the reversal of differentiation An integral can either be indefinite while it has no numerical value or may definite while have specific numerical values Integration is represented by the sign ?f(x)dx.

Rules of integration

i.The integral of a constant

?adx = ax +c;    whereas; a = constant


Find the following

a)  ?23dx

b)  ??2dx  ; whereas ? is a variable independent of x, hence it is treated as a constant.



i.  ?23dx = 23x + c

ii. ??2dx. = ?2 x + c


ii.  The integral of x raised to the power n

?xn dx = 1/((n+1). xn+1+ c


Find the following integrals

a) ?x2dx

b) ?x-5/2 dx


i. ?x2dx = (1/3)x3 + c

ii.  ?x-5/2 dx = -(2/3)x3/2 + c


iii). Integral of a constant times a function

? af(x) dx = a ? f(x) dx


Determine the given integrals:




a). ?ax3dx = a ? x3 dx

= (a/4) x4 + c

b). ?20x5dx = 20 ?20x5dx

= (10/3) x6 +c

iv). Integral of sum of two or more functions

?{f(x) + g(x)} dx = ?f(x)dx + ?g(x) dx

?{f(x) + g(x) + h(x)}dx = ?f(x)dx + ?g(x)dx + ?h(x)dx


Find the given

i.          ?(4x2 + ½ x-3) dx

ii.         ?(x3/4  + 3/7 x- ½ + x5)





1987_integration 1.png

v. Integral of a difference

?{f(x) - g(x)} dx = ?f(x)dx - ?g(x) dx

Posted Date: 2/15/2013 6:59:42 AM | Location : United States

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