Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
cos 3x cos 2x
Advertisements
Solution
`int cos 3x cos 2x "d"x = int 1/2 (2 cos 3x cos 2x) "d"x`
= `1/2 int [cos(3x + 2x) + cos(3x - 2x)] "d"x`
= `1/2 int (cos 5x + cos x) "d"x`
= `1/2 [int cos 5x "d"x + int cos x "d"x]`
= `1/2 [(sin 5x)/5 + sin x] + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
x sec x tan x
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
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 ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
