मराठी

Aafd∫-aaf(x)dx = 0 if f is an ______ function. - Mathematics

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प्रश्न

`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.

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उत्तर

`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an Odd function.

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पाठ 7: Integrals - Solved Examples [पृष्ठ १६३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 7 Integrals
Solved Examples | Q 30 | पृष्ठ १६३

संबंधित प्रश्‍न

Evaluate : `int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`


 
 

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

 
 

By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2)  sqrt(sinx)/(sqrt(sinx) + sqrt(cos x)) dx` 


By using the properties of the definite integral, evaluate the integral:

`int_((-pi)/2)^(pi/2) sin^2 x  dx`


Evaluate the definite integrals `int_0^pi (x tan x)/(sec x + tan x)dx`


\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.


\[\int_\pi^\frac{3\pi}{2} \sqrt{1 - \cos2x}dx\]

Evaluate : `int _0^(pi/2) "sin"^ 2  "x"  "dx"`


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


`int_"a"^"b" "f"(x)  "d"x` = ______


`int_(-7)^7 x^3/(x^2 + 7)  "d"x` = ______


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`int_0^{pi/2} log(tanx)dx` = ______


`int_0^4 1/(1 + sqrtx)`dx = ______.


`int_2^3 x/(x^2 - 1)` dx = ______


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


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`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = ______


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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.


The value of `int_((-1)/sqrt(2))^(1/sqrt(2)) (((x + 1)/(x - 1))^2 + ((x - 1)/(x + 1))^2 - 2)^(1/2)`dx is ______.


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 ______.


With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.


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Evaluate the following integral:

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Evaluate the following integral:

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