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
Evaluate : `int1/(x(3+logx))dx`
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 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 2^(3x + 5) "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 x^2 cos x "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
