Advertisements
Advertisements
प्रश्न
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Advertisements
उत्तर
Let `I = int ((cos 2x - cos 2alpha)/(cos x - cos alpha)) dx`
`= int ((2 cos^2 x - 1) - (2 cos^2 alpha - 1))/(cos x - cos alpha) dx`
`= int (2(cos^2 x - cos^2 alpha))/ (cos x - cos alpha) dx`
`= int ((2 cos^2 x - 1) - (2 cos^2 alpha - 1))/(cos x - cos alpha) dx`
`= 2 int (cos x + cos alpha) dx`
`= 2 int (cos x) dx + int (2 cos alpha) dx`
`= 2 sin + 2x cos alpha + C`
`= 2 (sin x + x cos alpha) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
`(1-cosx)/(1 + cos x)`
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:
cos4 2x
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Find the integrals of the function:
sin−1 (cos x)
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`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 dx/(x^2 + 4x + 8)`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
