Advertisements
Advertisements
प्रश्न
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
Advertisements
उत्तर
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to e – 1.
Explanation:
Let I = `int_0^(pi/2) cos x "e"^(sinx) "d"x`
Put sin x = t
⇒ cos x "d"x` = dt
∴ I = `int_0^1 "e"^"t" "dt"`
= `["e"^"t"]_0^1`
= `"e"^1 - "e"^0`
= e – 1
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
Evaluate : `intsec^nxtanxdx`
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/2) (2log sin x - log sin 2x)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/2) (sin x - cos x)/(1+sinx cos x) dx`
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
Evaluate : `int "x"^2/("x"^4 + 5"x"^2 + 6) "dx"`
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
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 = ?
`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?
`int_0^{pi/2} xsinx dx` = ______
If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
The value of `int_1^3 dx/(x(1 + x^2))` is ______
`int_0^pi x*sin x*cos^4x "d"x` = ______.
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
If `intxf(x)dx = (f(x))/2` then f(x) = ex.
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.
`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.
The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.
`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is ______.
`int_1^2 x logx dx`= ______
Evaluate `int_0^3root3(x+4)/(root3(x+4)+root3(7-x)) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 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 integral:
`int_0^1x(1 - x)^5dx`
The value of \[\int_{-1}^{1}\left(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right)\mathrm{d}x\] is
