topmath.in

integration by parts method

evaluate the integral of (1+x) / x (x-2)^0.5
Express  the recurring decimal 0.484848... as a fraction
 using the concept of geometric series

--------------------------------------------------------------------

---------------------------------------------------------------------


evaluate the integral of (1+x) /[ x *sqrt(x-2)]


put u = sqrt(x-2)

or x = 2 + (u^2)
dx = 2udu

change everything in terms of u and integrate.

integration formula

integral of (1+x) / x (x-2)^0.5


----------------------------------------------------------------------

problem2

When a polynomial p(x) is divided by (x+1), the remainder is 4.
And when it is divided by (x-2), it's remainder is 3.
What is the remainder  when p(x) is divided by x²-x-2

given p(-1) = 4 , p(2) = 3   (remainders) ---------------------(1)

 note that   x²-x-2 = (x+1)(x-2)
let q(x) be the quotient and r(x) = ax + b be the remainder
(since you are dividing by a quadratic)
 when p(x) is divided by ( x²-x-2 )

therfore p(x) = (x+1)(x-2)q(x) + ax + b         --------------(2)

putting x = -1  and x = 2  in eqn(2)  and using eqn(1), we get

4 =  -a + b
3= 2a + b

solving,
 a = -1 / 3
 b = 11 /3

therefore remainder = ax + b  = (11- x)/3

-----------------------------------------------------------------------
problem

Express  the recurring decimal 0.484848... as a fraction
 using the concept of geometric series

rational number using infinite gp

other questions and problems:

*integral calculus integration formula





----------------------------------------------------------------------------------------------
trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
---------------------------------------------------------------------------------------
*HOME PAGE   * mathematical formulae  * Indices, surds and some identities:   * Quadratic equations  * Progression  *Analytical Geometry * Trigonometry formula
  *Laplace Transform Inverse laplace transform *Vector
---------------------------------------------

---------------------------------------------

* Complex Number  *Hyperbolic function
disclaimer:
There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work. Also some of the companies which are displaying
advertisements may install cookies on your computer and may be tracking your browsing habits.