Advertisements
Advertisements
प्रश्न
Evaluate the integral by using substitution.
`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`
Advertisements
उत्तर
Let `I = int_1^2 e^(2x) (1/x - 1/(2x^2)) dx`
Put 2x = t
⇒ 2dx = dt
When x = 1, t = 2
And when x = 2, t = 4
∴ `I = 1/2 int_2^4 e^t (2/t - (1 xx4)/(2t^2)) dt`
`= 1/2 int_2^4 e^t (2/t - 2/t^2) dt`
`= int_2^4 e^t* (1/t - 1/t^2) dt`
`= int_2^4 e^t *[1/t + d/dt (1/t)] dt`
`= [e^t * 1/t]_2^4 = 1/4 e^4 - e^2/2`
`= e^2/2 (e^2/2 - 1)`
or `(e^2 (e^2 - 2))/4`
APPEARS IN
संबंधित प्रश्न
Evaluate: `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate : `int1/(3+5cosx)dx`
Evaluate :
`∫_(-pi)^pi (cos ax−sin bx)^2 dx`
Evaluate: `intsinsqrtx/sqrtxdx`
Evaluate the integral by using substitution.
`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`
Evaluate the integral by using substitution.
`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`
The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.
If `f(x) = int_0^pi t sin t dt`, then f' (x) is ______.
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate the following definite 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 each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?
`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.
Evaluate the following:
`int "dt"/sqrt(3"t" - 2"t"^2)`
Find: `int (dx)/sqrt(3 - 2x - x^2)`
