Advertisements
Advertisements
प्रश्न
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
पर्याय
`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
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
Evaluate: `int_(-a)^asqrt((a-x)/(a+x)) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) dx`
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_(pi/2)^(pi/2) sin^7 x dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
Prove that `int_0^af(x)dx=int_0^af(a-x) dx`
hence evaluate `int_0^(pi/2)sinx/(sinx+cosx) dx`
Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
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_"a"^"b" "f"(x) "d"x` = ______
`int (cos x + x sin x)/(x(x + cos x))`dx = ?
`int_0^{pi/2} xsinx dx` = ______
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
`int_-1^1x^2/(1+x^2) dx=` ______.
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
`int_0^9 1/(1 + sqrtx)` dx = ______
`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.
`int_(-1)^1 (x + x^3)/(9 - x^2) "d"x` = ______.
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.
Evaluate:
`int_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`
`int (dx)/(e^x + e^(-x))` is equal to ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
Evaluate: `int_0^π x/(1 + sinx)dx`.
Evaluate the following integral:
`int_0^1 x(1 - 5)^5`dx
Evaluate the following integral:
`int_0^1x (1 - x)^5 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`
Evaluate the following integral:
`int_0^1x(1-x)^5dx`
