Advertisements
Advertisements
प्रश्न
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
विकल्प
`int_"a"^"b" "f"(x - "c")"d"x`
`int_"a"^"b" "f"(x + "c")"d"x`
`int_"a"^"b" "f"(x)"d"x`
`int_("a" - "c")^("b" - "c") "f"(x)"d"x`
Advertisements
उत्तर
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to `int_"a"^"b" "f"(x + "c")"d"x`.
Explanation:
Since by putting x = t + c, we get
I = `int_"a"^"b" "f"("c" + "t")"dt"`
= `int_"a"^"b" "f"(x + "c")"d"x`.
APPEARS IN
संबंधित प्रश्न
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) -2
(c) 2
(d) ±2
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/4) log (1+ tan x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` dx is ______.
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
Evaluate : `int _0^(pi/2) "sin"^ 2 "x" "dx"`
Evaluate : `int "e"^(3"x")/("e"^(3"x") + 1)` dx
Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`
Find `dy/dx, if y = cos^-1 ( sin 5x)`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
`int_0^1 ((x^2 - 2)/(x^2 + 1))`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_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?
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_0^4 1/(1 + sqrtx)`dx = ______.
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_(pi/18)^((4pi)/9) (2 sqrt(sin x))/(sqrt (sin x) + sqrt(cos x))` dx = ?
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
`int_{pi/6}^{pi/3} sin^2x dx` = ______
`int_0^9 1/(1 + sqrtx)` dx = ______
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
If `int_0^1 "e"^"t"/(1 + "t") "dt"` = a, then `int_0^1 "e"^"t"/(1 + "t")^2 "dt"` is equal to ______.
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
Evaluate: `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7) - x)dx`
`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.
The integral `int_0^2||x - 1| -x|dx` is equal to ______.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
Let `int ((x^6 - 4)dx)/((x^6 + 2)^(1/4).x^4) = (ℓ(x^6 + 2)^m)/x^n + C`, then `n/(ℓm)` is equal to ______.
If `lim_("n"→∞)(int_(1/("n"+1))^(1/"n") tan^-1("n"x)"d"x)/(int_(1/("n"+1))^(1/"n") sin^-1("n"x)"d"x) = "p"/"q"`, (where p and q are coprime), then (p + q) is ______.
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
\[\int_{-2}^{2}\left|x^{2}-x-2\right|\mathrm{d}x=\]
Which expression is equal to \[\frac{1}{1+\sqrt{\tan x}}\] in the evaluation of \[\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{\tan x}}\]?
