हिंदी

Afdafd∫02af(x)dx=2∫0af(x)dx, if f(2a – x) = ______.

Advertisements
Advertisements

प्रश्न

`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.

रिक्त स्थान भरें
Advertisements

उत्तर

`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = f(x).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Solved Examples [पृष्ठ १६३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 7 Integrals
Solved Examples | Q 31 | पृष्ठ १६३

संबंधित प्रश्न

If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`

(A) 1

(B) 2

(C) –1

(D) –2


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(3+log x))dx` 


Evaluate : `int 1/("x" [("log x")^2 + 4])  "dx"`


Evaluate : `int  "e"^(3"x")/("e"^(3"x") + 1)` dx


Evaluate: `int_0^pi ("x"sin "x")/(1+ 3cos^2 "x") d"x"`.


Find : `int_  (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.


`int_0^2 e^x dx` = ______.


`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______ 


`int_-9^9 x^3/(4 - x^2)` dx = ______


`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.


The value of `int_1^3 dx/(x(1 + x^2))` is ______ 


`int_-2^1 dx/(x^2 + 4x + 13)` = ______


`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`


`int_(pi/4)^(pi/2) sqrt(1-sin 2x)  dx =` ______.


`int_0^pi x*sin x*cos^4x  "d"x` = ______.


If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.


Evaluate: `int_1^3 sqrt(x)/(sqrt(x) + sqrt(4) - x) dx`


The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.


Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.


Let f be continuous periodic function with period 3, such that `int_0^3f(x)dx` = 1. Then the value of `int_-4^8f(2x)dx` is ______.


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 ______.


`int_0^(π/4) x. sec^2 x  dx` = ______.


`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.


Evaluate: `int_1^3 sqrt(x + 5)/(sqrt(x + 5) + sqrt(9 - x))dx`


Evaluate the following integral:

`int_0^1 x(1 - 5)^5`dx


`int_1^2 x logx  dx`= ______


Evaluate the following integral:

`int_-9^9 x^3/(4 - x^2) dx`


Evaluate the following integral:

`int_0^1 x(1 - x)^5 dx`


Evaluate the following integral:

`int_-9^9x^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`


\[\int_{-2}^{2}\left|x^{2}-x-2\right|\mathrm{d}x=\]


When is \[P_4\] : Special Case of \[P_3\] applied?


Why can \[\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^{2}x\,dx\] be written as \[2\int_{0}^{\frac{\pi}{4}}\sin^{2}x\,dx\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×