Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Advertisements
उत्तर
Let I = `intsin(x - a)/cos(x + b).dx`
= `int(sin[(x + b) - (a + b)])/cos(x + b).dx`
= `int[sin(x + b) cos(a + b) - cos(x + b)sin(a + b))/cos(x + b).dx`
= `int[(sin(x + b) cos(a + b))/cos(x + b) - (cos(x + b)sin(a + b))/cos(x + b)].dx`
= `cos (a + b) int tan (x + b) dx - sin (a + b) int 1dx`
= cos (a + b) log | sec (x + b) | – x sin (a + b) + c.
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`1/(x-sqrtx)`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of
Write a value of
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate `int 1/("x" ("x" - 1))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int (cos2x)/(sin^2x) "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x sqrt(1 + x^2) dx`
`int x^3 e^(x^2) dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
