मराठी

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) = ______.

रिकाम्या जागा भरा
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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Integrals - Solved Examples [पृष्ठ १६३]

APPEARS IN

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

संबंधित प्रश्‍न

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


 
 

Evaluate : `intlogx/(1+logx)^2dx`

 
 

 
 

Evaluate `int_(-2)^2x^2/(1+5^x)dx`

 
 

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

`int_0^4 |x - 1| dx`


Show that `int_0^a f(x)g (x)dx = 2 int_0^a f(x) dx`  if f and g are defined as f(x) = f(a-x) and g(x) + g(a-x) = 4.


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


Evaluate  : `int "x"^2/("x"^4 + 5"x"^2 + 6) "dx"`


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


Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x))  "d"x`


Evaluate `int_0^1 x(1 - x)^5  "d"x`


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


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


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


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


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


If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.


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


`int_0^1 "e"^(5logx) "d"x` = ______.


`int_(-1)^1 (x + x^3)/(9 - x^2)  "d"x` = ______.


Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`


Show that `int_0^(pi/2) (sin^2x)/(sinx + cosx) = 1/sqrt(2) log (sqrt(2) + 1)`


Evaluate:

`int_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`


Evaluate: `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7) - 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`


If `int_(-a)^a(|x| + |x - 2|)dx` = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then `int_a^(-a)(x + [x])dx` is equal to ______.


`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.


If f(x) = `{{:(x^2",", "where"  0 ≤ x < 1),(sqrt(x)",", "when"  1 ≤ x < 2):}`, then `int_0^2f(x)dx` equals ______.


If `int_0^(π/2) log cos x  dx = π/2 log(1/2)`, then `int_0^(π/2) log sec dx` = ______.


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


Evaluate `int_-1^1 |x^4 - x|dx`.


If `int_0^(2π) cos^2 x  dx = k int_0^(π/2) cos^2 x  dx`, then the value of k is ______.


`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.


Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.


Evaluate the following limit :

`lim_("x"->3)[sqrt("x"+6)/"x"]`


Evaluate the following integral:

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


`∫_0^(π/2) (sqrttan x + sqrtcot x)dx` = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×