Advertisements
Advertisements
प्रश्न
Integrate the function:
`1/(xsqrt(ax - x^2)) ["Hint : Put x" = a/t]`
Advertisements
उत्तर
Let `1/(xsqrt(ax - x^2))`
Put `x = a/t`
dx = `- a/t^2 dt`
Now, `xsqrt(ax - x^2) = a/tsqrt(a xx a/t - a^2/t^2)`
`= a^2/t sqrt(1/t - 1/t^2) = a^2/t^2 sqrt(t - 1)`
`therefore I = 1/(a^2/t^2 sqrt(t - 1)) xx (- a)/t^2 dt`
`= - 1/a int 1/sqrt(t - 1) dt`
`= - 1/a ((t - 1)^(- 1/2 + 1))/(- 1/2 + 1) + C`
`= - 1/a (t - 1)^(1/2)/(1/2) + C`
`= - 2/a sqrt(t - 1) + C`
`= - 2/a sqrt(a/x - 1) + C`
`= - 2/a sqrt((a - x)/x) + C`
APPEARS IN
संबंधित प्रश्न
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
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.
(axe + b)2
Find an antiderivative (or integral) of the following function by the method of inspection.
sin 2x – 4 e3x
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int(1 - x) sqrtx dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
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:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`x^3/(sqrt(1-x^8)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`sqrt((1-sqrtx)/(1+sqrtx))`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
If `d/(dx) f(x) = 4x^3 - 3/x^4`, such that `f(2) = 0`, then `f(x)` is
`int (dx)/(sin^2x cos^2x) dx` equals
`int (dx)/sqrt(9x - 4x^2)` equal
`int (dx)/sqrt(9x - 4x^2)` equals
`int (dx)/(x(x^2 + 1))` equals
`int x^2 e^(x^3) dx` equals
`int e^x sec x(1 + tanx) dx` equals
`int sqrt(x^2 - 8x + 7) dx` is equal to:-
What is anti derivative of `e^(2x)`
If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.
If y = `x^((sinx)^(x^((sinx)^(x^(...∞)`, then `(dy)/(dx)` at x = `π/2` is equal to ______.
Anti-derivative of `(tanx - 1)/(tanx + 1)` with respect to x is ______.
