Advertisements
Advertisements
प्रश्न
Evaluate the integral by using substitution.
`int_0^1 x/(x^2 +1)`dx
Advertisements
उत्तर
Let `int_0^1 x/(x^2 + 1) dx`
Put x2 + 1 = t
2x dx = dt
When x =1, t = 2; x = 0, t = 1
`therefore I = int_1^2 dt/t`
∴ `I = 1/2 int_1^2 dt/t = [1/2 log t]_1^2`
`= 1/2 [log 2 - log 1]`
`= 1/2 log 2`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int (1+logx)/(x(2+logx)(3+logx))dx`
find `∫_2^4 x/(x^2 + 1)dx`
Evaluate: `intsinsqrtx/sqrtxdx`
Evaluate the integral by using substitution.
`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`
Evaluate the integral by using substitution.
`int_(-1)^1 dx/(x^2 + 2x + 5)`
Evaluate the integral by using substitution.
`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`
The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.
Evaluate of the following integral:
(i) \[\int x^4 dx\]
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate :
Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .
Evaluate: `int_ e^x ((2+sin2x))/cos^2 x dx`
`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?
`int_0^1 x(1 - x)^5 "dx" =` ______.
The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is
Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.
Evaluate: `int x/(x^2 + 1)"d"x`
If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.
