मराठी

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

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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 Exemplar [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`


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

`int_0^(pi/2) cos^2 x dx`


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

`int_0^a  sqrtx/(sqrtx + sqrt(a-x))   dx`


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


Evaluate :  `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`


Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`


`int_1^2 1/(2x + 3)  dx` = ______


`int_2^4 x/(x^2 + 1)  "d"x` = ______


The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x2). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.


`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______


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


`int_0^{pi/2} xsinx dx` = ______


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


`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________


`int_(pi/18)^((4pi)/9) (2 sqrt(sin x))/(sqrt (sin x) + sqrt(cos x))` dx = ?


f(x) =  `{:{(x^3/k;       0 ≤ x ≤ 2), (0;     "otherwise"):}` is a p.d.f. of X. The value of k is ______


`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______ 


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


Evaluate `int_(-1)^2 "f"(x)  "d"x`, where f(x) = |x + 1| + |x| + |x – 1|


Evaluate the following:

`int_0^(pi/2)  "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos4x)


`int_((-pi)/4)^(pi/4) "dx"/(1 + cos2x)` is equal to ______.


Evaluate: `int_(-1)^3 |x^3 - x|dx`


If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0

⇒ `1/4 (square - square)` = 0

⇒ b4 – `square` = 0

⇒ (b2 – a2)(`square` + `square`) = 0

⇒ b2 – `square` = 0 as a2 + b2 ≠ 0

⇒ b = ± `square`


Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.


`int_0^1|3x - 1|dx` equals ______.


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 ______.


`int_0^(pi/4) (sec^2x)/((1 + tanx)(2 + tanx))dx` equals ______.


If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.


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


Evaluate: `int_0^π x/(1 + sinx)dx`.


Evaluate: `int_0^(π/4) log(1 + tanx)dx`.


Solve the following.

`int_1^3 x^2 logx  dx`


Evaluate `int_1^2(x+3)/(x(x+2))  dx`


Evaluate the following definite integral:

`int_1^3 log x  dx`


Solve the following.

`int_0^1e^(x^2)x^3dx`


`int_(pi"/"11)^(9pi"/"22) (dx)/(1 + sqrttan x)` =


Which formula expresses \[P_1\] : Reversing Limits?


Which property is useful for piecewise functions or modulus (absolute value) functions?


If \[I=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{\tan x}}\], what is the value of \[I\]?


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