Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
उत्तर
Let `I = int (sin^-1 x)/sqrt(1 - x^2)` dx
Put sin-1 x = t
`1/sqrt(1 - x^2)` dx = dt
Hence, `I = int t dt`
`=1/2t^2 + C`
`=1/2 (sin^-1 x)^2 + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int \log_e x\ dx\].
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int cos sqrtx` dx = _____________
`int(log(logx))/x "d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
`int "cosec"^4x dx` = ______.
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`intsqrt(sec x/2 - 1)dx`
