Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Advertisements
उत्तर
`int((cos2x - cos2 alpha)/(cosx - cos alpha)) "d"x`
= `int [((2 cos^2x - 1) - (2cos^2alpha - 1))/(cosx - cosalpha)]* "d"x`
cos 2x = cos2x – sin2x – 1
cos 2x = 2 cos2x – 1
= `int (2cos^2x - 1 - 2cos^2alpha + 1)/(cosx - cosalpha) * "d"x`
= `int (2cos^x - 2cos^2alpha)/(cosx - cosalpha) * "d"x`
= `int (2(cos^2x - cos^2alpha))/(cosx - cosalpha) * "d"x`
= `2 int [((cosx + cosalpha)(cosx - cosalpha))/(cosx - cosalpha)] * "d"x`
= `2 int(cosx + cosalpha) "d"x`
= `2 int cos x "d"x + 2 int cos alpha "d"x`
= `2 int cos x "d"x + 2 int cos alpha int "d"x`
= 2 sin x + 2 cos α(x) + c
= 2 sin x + 2x cos α + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
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
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
