Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Advertisements
उत्तर
`int sqrt(x^2 - 2x - 3) "d"x = int sqrt((x - 1)^2 - 1^2 - 3) "d"x`
= `int sqrt((x - 1)^2 - 4) "d"x`
= `int sqrt((x - 1)^2 - 2^2) "d"x`
Put x – 1 = t
dx = dt
= `int sqrt("t"^2 - 2^2) "dt"`
= `"t"/2 sqrt("t"^2 - 2^2) - 2^2/2 log |"t" + sqrt("t"^2 - 2^2)| + "c"`
= `(x - 1)/2 sqrt((x - 1)^2 - 4) - 2 log|x - 1 + sqrt((x - 1)^2 - 4)| + "c"`
= `(x - 1)/2 sqrt(x^2 - 2x + 1 - 4) - 2 log|x - 1 sqrt(x^2 - 2x + 1 - 4) | + "c"`
`int sqrt(x^2 - 2x - 3) "d"x = (x - 1)/2 sqrt(x^2 - 2x - 3) - 2 log |x - 1 + sqrt(x^2 - 2x - 3)| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
