Advertisements
Advertisements
Question
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Advertisements
Solution
`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
RELATED QUESTIONS
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.
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
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 sqrt((1 - x)/(1 + x)) "d"x` is
