Integration-mathematics, Mathematics

Assignment Help:

Integration

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

Illustration

Find the following

a)  ?23dx

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

 

Solution

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

Illustration

Find the following integrals

a) ?x2dx

b) ?x-5/2 dx

Solution

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

Illustration

Determine the given integrals:

i.?ax3dx

ii.?20x5dx

Solution

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

Illustration

Find the given

i.          ?(4x2 + ½ x-3) dx

ii.         ?(x3/4  + 3/7 x- ½ + x5)

Solution

 

5_integration.png

 

1987_integration 1.png

v. Integral of a difference

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


Related Discussions:- Integration-mathematics

Profit and loss, a shopkeeper buys two cameras at the same price . he sells...

a shopkeeper buys two cameras at the same price . he sells one camera at a profit of 18% and the other at a price of 10% less than the selling price of the first camera. find his p

Linear programming , Use the simplex method to solve the following LP Probl...

Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0

Solve by factorization, Solve by factorization X 2 +(a/a+b + a+b/a)x+...

Solve by factorization X 2 +(a/a+b + a+b/a)x+1 = 0 X 2 +(a/a+b + a+b/a)x+1 =>  X 2 +(a/a+b x a+b/ax + a/a+b .a+b/a) =>  X[x+a/a+b] +a+b/a[a+a*a+b]= 0 =>  X= -a

Correlation coefficient, Correlation coefficient - These are numerical...

Correlation coefficient - These are numerical measures of the correlations existing between the independent and the dependent variables - These are better measures of corre

Calculus, sin(xy)+x=5y Find the derivative.

sin(xy)+x=5y Find the derivative.

Full asymptotic expansion , Consider the integral where the notatio...

Consider the integral where the notation means a contour that is parallel to the real z axis, but moved down by a distance d . Use the method of steepest descents to deri

Why x and y are simplifying expressions, Why x and y are Simplifying Expres...

Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t

Introducing counting, INTRODUCING COUNTING : From what you studied previou...

INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd