Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(sin4x)/sinx`
उत्तर
`int (sin4x)/sinx "d"x = int (sin2(2x))/sinx * "d"x`
[sin 2A = 2 sin A cos A]
= `int (2sin 2x cos 2x)/sinx "d"x`
= `2 int (2sinx cosx * cos 2x)/sinx * "d"x`
= `4int cos 2x cos x * d"x`
= `2 int 2 cos 2x cosx * "d"x`
= `2 int [cos(2x + x) + cos(2x - x)] "d"x`
[2 cos A cos B = cos(A + B) + cos(A – B)]
= `2 int (cos 3x + cosx) "d"x`
= `2 int cos 3x "d"x + 2int cos x "d"x`
= `2 (sin3x)/3 + 2 sin x + "c"`
= `2 [(sin 3x)/3 + sin x] + "c"`
APPEARS IN
संबंधित प्रश्न
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.
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
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 :
`1/(x log x log (log x))`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
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:
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 sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
