Advertisements
Advertisements
प्रश्न
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Advertisements
उत्तर
Let f(x) = `log((2 - x)/(2 + x))`
We have, f(– x) = `log((2 + x)/(2 - x))`
= `-log((2 - x)/(2 + x))`
= – f(x)
So, f(x) is an odd function.
∴ `int_-1^1 log ((2 - x)/(2 + x))dx` = 0.
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
Evaluate `int_(-2)^2x^2/(1+5^x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
Evaluate = `int (tan x)/(sec x + tan x)` . dx
`int_0^1 "e"^(2x) "d"x` = ______
`int_1^2 1/(2x + 3) dx` = ______
`int_2^4 x/(x^2 + 1) "d"x` = ______
Evaluate `int_0^1 x(1 - x)^5 "d"x`
`int (cos x + x sin x)/(x(x + cos x))`dx = ?
The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x2). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.
The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on ______.
`int_0^{pi/2} xsinx dx` = ______
The value of `int_1^3 dx/(x(1 + x^2))` is ______
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
`int_0^9 1/(1 + sqrtx)` dx = ______
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
`int_0^(pi/2) sqrt(1 - sin2x) "d"x` is equal to ______.
Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
If f(x) = `(2 - xcosx)/(2 + xcosx)` and g(x) = logex, (x > 0) then the value of the integral `int_((-π)/4)^(π/4) "g"("f"(x))"d"x` is ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.
`int_0^(π/4) x. sec^2 x dx` = ______.
`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.
Evaluate: `int_0^π x/(1 + sinx)dx`.
What is the value of a definite integral when its upper and lower limits are equal?
Which expression equals \[\int_{a}^{b} f(x)\,dx\] by \[P_3\] : The "King's Rule"?
When is \[P_4\] : Special Case of \[P_3\] applied?
