Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Advertisements
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
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve 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 "e"^(sqrt(x)) "d"x` is
