English

Ndnn∫0π2sinnxdxsinnx+cosnx = ______. - Mathematics

Advertisements
Advertisements

Question

`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.

Fill in the Blanks

Solution

`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = `pi/4`.

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Solved Examples [Page 163]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 7 Integrals
Solved Examples | Q 32 | Page 163

RELATED QUESTIONS

 
 

Evaluate : `intlogx/(1+logx)^2dx`

 
 

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

`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`


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

`int_0^pi log(1+ cos x) 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.


The value of `int_0^(pi/2) log  ((4+ 3sinx)/(4+3cosx))` dx is ______.


`∫_4^9 1/sqrtxdx=`_____

(A) 1

(B) –2

(C) 2

(D) –1


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


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


`int_0^(pi/4) (sec^2 x)/((1 + tan x)(2 + tan x))`dx = ?


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


Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`


`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.


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


`int (dx)/(e^x + e^(-x))` is equal to ______.


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


`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 ______.


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


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 ______.


Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.

Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.


Evaluate the following definite integral:

`int_4^9 1/sqrt"x" "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`


Solve.

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


Solve the following.

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


Evaluate:

`int_0^sqrt(2)[x^2]dx`


Evaluate the following integral:

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


Evaluate the following integral:

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


Evaluate the following definite integral:

`int_-2^3(1)/(x + 5)  dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×