Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Advertisements
उत्तर
`int sqrt(9 - (2x + 5)^2) "d"x = int sqrt(3^2 - (2x + 5)^2) "d"x`
Put 2x + 5 = t
2 dx = dt
dx = `1/2 "dt"`
= `int sqrt(3^2 - "t"^2) xx 1/2 "dt"`
= `1/2 int sqrt(3^2 - "t"^2) "dt"`
= `1/2 ["t"/2 sqrt(3^2 - "t"^2) + 3^2/2 sin^-1 ("t"/3) + "c"]`
= `1/4 [(2x + 5) sqrt(9 - (2x + 5)^2) + 9 sin^-1 ((2x + 5)/3)] + "c"`
`int sqrt(9 - (2x + 5)^2) "d"x = 1/4 [(2x + 5) sqrt(9 - (2x + 5)^2) + 9 sin^-1 ((2x + 5)/3)] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
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:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
