English

∫011-x1+ x dx = - Mathematics and Statistics

Advertisements
Advertisements

Question

`int_0^1 sqrt((1 - x)/(1 +  x))  "d"x` =

Options

  • `pi/2 - 1`

  • `pi/2 + 1`

  • `pi/2 - 2`

  • `p/2 + 2`

MCQ

Solution

`pi/2 - 1`

shaalaa.com
Fundamental Theorem of Integral Calculus
  Is there an error in this question or solution?
Chapter 2.4: Definite Integration - MCQ

RELATED QUESTIONS

Evaluate : `int_2^3 (1)/(x^2 + 5x + 6)*dx`


Evaluate : `int_0^(pi/4) sin 4x sin 3x *dx`


Evaluate:

`int_0^(pi/4) sqrt(1 + sin 2x)*dx`


Evaluate : `int_0^(1/sqrt(2)) (sin^-1x)/(1 - x^2)^(3/2)*dx`


Evaluate : `int_0^(pi//4) (sin2x)/(sin^4x + cos^4x)*dx`


Evaluate : `int_0^(pi/4) (cosx)/(4 - sin^2x)*dx`


Evaluate:

`int_0^1 sqrt((1 - x)/(1 + x)) * dx`


Evaluate the following : `int_0^1 (log(x + 1))/(x^2 + 1)*dx`


Evaluate the following : `int_0^pi x sin x cos^2x*dx`


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


`int_0^(log5) (e^x sqrt(e^x - 1))/(e^x + 3) * dx` = ______.


Choose the correct option from the given alternatives : 

`int_1^2 (1)/x^2 e^(1/x)*dx` = 


Choose the correct option from the given alternatives :

`int_0^9 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx` =


Choose the correct option from the given alternatives :

The value of `int_((-pi)/4)^(pi/4) log((2+ sin theta)/(2 - sin theta))*d theta` is


Evaluate the following : `int_0^4 [sqrt(x^2 + 2x + 3]]^-1*dx`


Evaluate the following : if `int_a^a sqrt(x)*dx = 2a int_0^(pi/2) sin^3x*dx`, find the value of `int_a^(a + 1)x*dx`


Evaluate the following definite integrals: `int_2^3 x/(x^2 - 1)*dx`


Evaluate the following definite integrals: `int_2^3 x/((x + 2)(x + 3)). dx`


Evaluate the following definite integrals: if `int_1^"a" (3x^2 + 2x + 1)*dx` = 11, find a.


Evaluate the following definite integral:

`int_1^3 logx.dx`


Choose the correct alternative :

`int_"a"^"b" f(x)*dx` =


Solve the following : `int_2^3 x/((x + 2)(x + 3))*dx`


Solve the following : `int_(-2)^3 (1)/(x + 5)*dx`


Solve the following : `int_0^1 (1)/(2x - 3)*dx`


`int_1^9 (x + 1)/sqrt(x)  "d"x` =


Choose the correct alternative:

`int_4^9 ("d"x)/sqrt(x)` =


If `int_0^"a" (2x + 1)  "d"x` = 2, find a


By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2))  "d"x`

Solution: Let I = `int_1^2 (x + 3)/(x(x + 2))  "d"x`

Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`

∴ x + 3 = A(x + 2) + B.x

∴ A = `square`, B = `square`

∴ I = `int_1^2[("( )")/x + ("( )")/((x + 2))] "d"x`

∴ I = `[square log x + square log(x + 2)]_1^2`

∴ I = `square`


Evaluate the following definite intergral:

`int_-2^3 1/(x+5)  dx`


Evaluate the following definite integral:

`int_1^2 (3x)/((9x^2 - 1))dx`


Evaluate the following definite integral:

`int_-2^3 1/(x+5) *dx`


If `int_((-pi)/4) ^(pi/4) x^3 * sin^4 x  dx` = k then k = ______.


Evaluate the following definite integral:

`int_4^9 1/sqrtx dx`


Solve the following.

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


Evaluate the following definite integrals: `int_4^9 (1)/sqrt(x)*dx`


Solve the following.

`int_1^3x^2logx  dx`


Evaluate the following definite integral:

`int_-2^3 1/(x+5).dx`


Solve the following.

`int_1^3 x^2 logxdx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×