Advertisements
Advertisements
प्रश्न
`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.
Advertisements
उत्तर
`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = `pi/4`.
APPEARS IN
संबंधित प्रश्न
By using the properties of the definite integral, evaluate the integral:
`int_(-5)^5 | x + 2| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^1 x(1-x)^n dx`
By using the properties of the definite integral, evaluate the integral:
`int_((-pi)/2)^(pi/2) sin^2 x 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 ______.
\[\int\limits_0^k \frac{1}{2 + 8 x^2} dx = \frac{\pi}{16},\] find the value of k.
`int_0^2 e^x dx` = ______.
`int_1^2 1/(2x + 3) dx` = ______
`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan x))`dx = ?
`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?
`int_-9^9 x^3/(4 - x^2)` dx = ______
`int_0^1 (1 - x)^5`dx = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_0^pi x*sin x*cos^4x "d"x` = ______.
`int_0^pi x sin^2x dx` = ______
Evaluate `int_(-1)^2 "f"(x) "d"x`, where f(x) = |x + 1| + |x| + |x – 1|
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
`int_0^(pi/2) sqrt(1 - sin2x) "d"x` is equal to ______.
Evaluate: `int_0^(2π) (1)/(1 + e^(sin 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 value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is ______.
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 ______.
What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?
With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Evaluate the following integral:
`int_-9^9 x^3 / (4 - x^2) dx`
Evaluate the following integrals:
`int_-9^9 x^3/(4 - x^3 ) dx`
Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`
Evaluate the following definite intergral:
`int_1^3logx dx`
`∫_0^(π/2) (sqrttan x + sqrtcot x)dx` = ______.
`int_0^(pi/4) (cos^2 x)/(cos^2 x + 4 sin^2 x) dx` =
Which formula expresses \[P_1\] : Reversing Limits?
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"?
