Advertisements
Advertisements
प्रश्न
`int_(-5)^5 x^7/(x^4 + 10) dx` = ______.
पर्याय
10
5
0
`1/5`
उत्तर
`int_(-5)^5 x^7/(x^4 + 10) dx` = 0.
Explanation:
Let f(x) = `x^7/(x^4 + 10)`
∴ f(– x) = `(-x)^7/((-x)^4 + 10) = (-x^7)/(x^4 + 10)`
= – f(x)
∵ f(– x) = – f(x)
∴ f(x) is an odd function
∴ `int_(-a)^a f(x).dx` = 0
⇒ `int_(-5)^5 x^7/(x^4 + 10) dx` = 0
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsec^nxtanxdx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sqrt(sinx)/(sqrt(sinx) + sqrt(cos x)) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Evaluate : `int "x"^2/("x"^4 + 5"x"^2 + 6) "dx"`
Evaluate = `int (tan x)/(sec x + tan x)` . dx
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_"a"^"b" "f"(x) "d"x` = ______
`int_0^1 "e"^(2x) "d"x` = ______
`int_2^4 x/(x^2 + 1) "d"x` = ______
Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x)) "d"x`
`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan 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 ______.
`int_0^{pi/2} log(tanx)dx` = ______
`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`int_0^1 (1 - x)^5`dx = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
f(x) = `{:{(x^3/k; 0 ≤ x ≤ 2), (0; "otherwise"):}` is a p.d.f. of X. The value of k is ______
`int_0^{pi/2} cos^2x dx` = ______
`int_0^1 x tan^-1x dx` = ______
`int_0^9 1/(1 + sqrtx)` dx = ______
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
`int_(-1)^1 (x + x^3)/(9 - x^2) "d"x` = ______.
Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
Evaluate the following:
`int_(-pi/4)^(pi/4) log|sinx + cosx|"d"x`
`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
`int (dx)/(e^x + e^(-x))` is equal to ______.
Evaluate: `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tanx)`
Evaluate: `int_0^(2π) (1)/(1 + e^(sin x)`dx
`int_0^1 1/(2x + 5) dx` = ______.
If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0
⇒ `1/4 (square - square)` = 0
⇒ b4 – `square` = 0
⇒ (b2 – a2)(`square` + `square`) = 0
⇒ b2 – `square` = 0 as a2 + b2 ≠ 0
⇒ b = ± `square`
`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.
If `int_0^1(sqrt(2x) - sqrt(2x - x^2))dx = int_0^1(1 - sqrt(1 - y^2) - y^2/2)dy + int_1^2(2 - y^2/2)dy` + I then I equal.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
The value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.
Evaluate: `int_0^π x/(1 + sinx)dx`.
If `int_0^1(3x^2 + 2x+a)dx = 0,` then a = ______
`int_1^2 x logx dx`= ______
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Solve the following.
`int_0^1e^(x^2)x^3 dx`
Evaluate the following integral:
`int_-9^9 x^3 / (4 - x^2) dx`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
