Advertisements
Advertisements
प्रश्न
Find the integrals of the function:
cos 2x cos 4x cos 6x
Advertisements
उत्तर
Let `I = int cos 2x cos 4x cos 6x` dx
`= 1/2 int (2 cos 2x cos 4x) cos 6x dx`
... [∵ 2 cos A cos B = cos (A + B) - cos (A - B)]
`= 1/2 int (cos 6x + cos 2x) cos 6x dx`
`= 1/4 int 2 cos^2 6x dx + 1/4 int (2 cos 2c cos 6x) dx`
`= 1/4 int (1 + cos 12 x) dx + 1/4 int (cos 8x + cos 4x)` dx
`= 1/4 x + 1/4 ((sin 12x)/12) + 1/4 ((sin 8x)/8 + (sin 4x)/4) + C`
`= 1/4 [x + 1/12 sin 12 x + 1/8 sin 8x + 1/4 sin 4x] + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
sin4 x
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
tan3 2x sec 2x
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Find `int dx/(x^2 + 4x + 8)`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Evaluate `int_0^(3/2) |x sin pix|dx`
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
`int sinx/(3 + 4cos^2x) "d"x` = ______.
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
