Advertisements
Advertisements
प्रश्न
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Advertisements
उत्तर
Let `I = int (x cos^-1 x)/sqrt(1-x^2) dx`
Put cos-1 x = t
`- 1/sqrt(1-x^2) dx = dt`
`therefore I = - int t cos t dt`
`= - [t int cos t dt - int (d/dt (t)* int cos t dt) dt]`
`= -t sin t + int sin t dt = -t sint - cos t + C`
`= -t sqrt (1 - cos^2 t) - cos t + C`
`= - cos^-1 x sqrt (1 - x^2) - x + C`
`= -[cos^-1 x* sqrt (1 - x^2) + x] + C`
APPEARS IN
संबंधित प्रश्न
Prove that:
`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x sin 3x.
Integrate the function in x log 2x.
Integrate the function in tan-1 x.
Integrate the function in ex (sinx + cosx).
Evaluate the following: `int x.sin^-1 x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following w.r.t.x : e2x sin x cos x
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
`int sin4x cos3x "d"x`
Evaluate `int 1/(x log x) "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
∫ log x · (log x + 2) dx = ?
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
`int tan^-1 sqrt(x) "d"x` is equal to ______.
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
`int 1/sqrt(x^2 - 9) dx` = ______.
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
`int(logx)^2dx` equals ______.
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
Evaluate :
`int(4x - 6)/(x^2 - 3x + 5)^(3/2) dx`
`int1/sqrt(x^2 - a^2) dx` = ______
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!))dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`int x^3 e^(x^2) dx`
