Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Solution
`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
RELATED QUESTIONS
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
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:
x3 sin x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
