English

Choose the correct alternative: ∫23xx2-1 dx = - Mathematics and Statistics

Advertisements
Advertisements

Question

Choose the correct alternative:

`int_2^3 x/(x^2 - 1)  "d"x` =

Options

  • `log (8/3)`

  • `- log (8/3)`

  • `1/2 log(8/3)`

  • `-1/2 log(8/3)`

MCQ

Solution

`1/2 log(8/3)`

shaalaa.com
Fundamental Theorem of Integral Calculus
  Is there an error in this question or solution?
Chapter 1.6: Definite Integration - Q.1

RELATED QUESTIONS

 Show that: `int _0^(pi/4) log (1 + tanx) dx = pi/8 log2`


Evaluate : `int_0^4 (1)/sqrt(4x - x^2)*dx`


Evaluate:

`int_0^1 (1)/sqrt(3 + 2x - x^2)*dx`


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


Evaluate the following : `int_0^(pi/2) 1/(6 - cosx)*dx`


Evaluate the following : `int_(pi/5)^((3pi)/10) sinx/(sinx + cosx)*dx`


Evaluate the following definite integral:

`int_1^3 logx.dx`


Evaluate the following integrals : `int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx`


Choose the correct alternative :

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


State whether the following is True or False : `int_(-5)^(5)  x^3/(x^2 + 7)*dx` = 0


Solve the following : `int_2^3 x/(x^2 + 1)*dx`


`int_1^9 (x + 1)/sqrt(x)  "d"x` =


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


Prove that: `int_"a"^"b" "f"(x)  "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`


If `int_1^"a" (3x^2 + 2x + 1)  "d"x` = 11, find the real value of 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`


`int_0^(pi/2) root(7)(sin x)/(root(7)(sin x) + root(7)(cos x))`dx = ?


Evaluate the following definite integral :

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


Solve the following.

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


Evaluate:

`int_(-π/2)^(π/2) (sin^3x)/(1 + cos^2x)dx`


Prove that `int_0^(2a) f(x)dx = int_0^a[f(x)  + f(2a - x)]dx`


Evaluate the following definite intergral:

`int_4^9 1/sqrtxdx`


Solve the following.

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


Evaluate the following definite intergral:

`int_1^3 log x·dx`


Evaluate the integral.

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


Evaluate the following definite integral:

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


Evaluate the following definite intergral:

`\underset{4}{\overset{9}{int}}1/sqrt(x)dx`


Evaluate the following definite intergral:

`int_4^9(1)/sqrtxdx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×