IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

shinee

integrate the following

1/root(3-x²+2x)dx

mukulss

see shreya,,,,,,,,,

these type of questions form the basics of integration:

see the solluiton:

I = dx
--------------
sqrt [ 4 - (x-1)^2 ]

hope u r easily able to write the above step

now
very standard:

see:

let ::::: x-1 = t

dx = dt

so ur:

I = dt
---------------
sqrt [ 2^2 - t^2 ]

now easy....
i took alot of space to write thsi que so that u understand it properly

chinmay_saxena01

sol: first make perfect square in den. so that the question is converted in to standard form....
so we get ....1/root[(2)^2-(x-1)^2].........................(1)

let x-1 =t
differentiate w.r.t x so we get dx=dt.......
now apply this to eqn 1
and finally apply formula
1/a^2-x^2dx = 1/2alog(a+x/a-x)....hope i helped u,,,,,,,,,,,

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