Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
उत्तर
`int (sin sqrt(x))/sqrt(x) * "d"x`
Put `sqrt(x)` = u
`x^(1/2)` = u
`1/2 x^(1/2 - 1) "d"x` = du
`1/2 x^(- 1/2) "d"x` = du
`1/(2 x^(1/2)) "d"x` = du
`1/(2sqrt(x)) "d"x` = du
`1/sqrt(x) "d"x` = du
`int sin sqrt(x) * 1/sqrt(x) "d"x = int sin "u" 2 "du"`
= `2 int sin "u" "du"`
= `2 xx - cos "u" + "c"`
`int (sin sqrt(x))/sqrt(x) * "d"x = - 2 cos sqrt(x) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
