Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
x sin 3x
Advertisements
उत्तर
`int x sin 3x "d"x`
`int "u" "dv" = "uv" - "u""'""v"_1 + "u""'""v"_2 - "u""'""v"_3 +` ..........(1)
u = x
u' = 1
u" = 0
v1 = `int "v" "d"x``
= `int - (cos 3x)/3`
= `- 1/3 xx (sin 3x)/3`
v2 = `int "v"_1 "d"x`
= `int - 1/3^2 sin3x * "d"x`
= `- 1/3^2 xx 1/3 xx - cos 3x`
= `1/3^2 cos 3x`
`int x sin x "d"x = x xx - (cos3x)/3 - 1 xx - 1/3^2 sin 3x + 0 xx 1/3^3 cos3x + "c"`
`int x sin 3x "d"x = - x/3 cos 3x + 1/9 sin 3x + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
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 :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
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 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
