Advertisements
Advertisements
प्रश्न
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
उत्तर
Let I = `int (cos x)/sqrt(4 - sin^2 x)`dx
Substituting sin x = 2t
cos x dx = 2 dt
Hence, `I = int (2 dt)/sqrt(4 - 4t^2)`
`= int (2 dt)/(2sqrt(1 - t^2))`
`= int 1/sqrt(1 - t^2) dt = sin^-1 t + C`
`= sin^-1 ((sin x)/2) + C ....[(because sin x = 2 t), (=> t = (sin x)/2)]`
APPEARS IN
संबंधित प्रश्न
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find the following integrals:
`int (4e^(3x) + 1)`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
Find the following integrals:
`int(sec^2x)/(cosec^2x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(x - x^3)`
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
Integrate the function:
`(5x)/((x+1)(x^2 +9))`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
`1/((x^2 + 1)(x^2 + 4))`
Integrate the function:
`e^(3log x) (x^4 + 1)^(-1)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`1/sqrt(sin^3 x sin(x + alpha))`
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`f x^2 e^(x^3) dx` equals
`int e^x sec x(1 + tanx) dx` equals
What is anti derivative of `e^(2x)`
`d/(dx)x^(logx)` = ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
