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

Advertisements
Advertisements
MCQ

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)`

Advertisements

Solution

`1/2 log(8/3)`

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


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


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


Evaluate : `int_0^(2pi) sqrt(cos x) sin^3x*dx`


Evaluate : `int_0^(pi/2) (1)/(5 + 4 cos x)*dx`


Evaluate : `int_(-1)^1 (1)/(a^2e^x + b^2e^(-x))*dx`


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


Evaluate : `int_0^(pi/2) sin2x*tan^-1 (sinx)*dx`


Evaluate : `int_1^3 (cos(logx))/x*dx`


Evaluate : `int_0^(pi/2) (sinx - cosx)/(1 + sinx cosx)*dx`


Evaluate the following : `int_0^3 x^2(3 - x)^(5/2)*dx`


Evaluate the following : `int_(-1)^(1) (x^3 + 2)/sqrt(x^2 + 4)*dx`


Evaluate the following : `int_(-a)^(a) (x + x^3)/(16 - x^2)*dx`


Evaluate the following : `int_0^1 t^2 sqrt(1 - t)*dt`


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


Choose the correct option from the given alternatives :

If `[1/logx - 1/(logx)^2]*dx = a + b/(log2)`, then


Evaluate the following : `int_(-1)^(1) (1 + x^3)/(9 - x^2)*dx`


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


Evaluate the following : `int_1^oo 1/(sqrt(x)(1 + x))*dx`


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


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


Evaluate the following : `int_0^(pi/4) (cos2x)/(1 + cos 2x + sin 2x)*dx`


Evaluate the following : `int_0^(pi/2) [2 log (sinx) - log (sin 2x)]*dx`


Evaluate the following : `int_0^pi  (sin^-1x + cos^-1x)^3 sin^3x*dx`


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


Evaluate the following : `int_(-2)^(3) |x - 2|*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 integrals : `int_0^1 log(1/x - 1)*dx`


Choose the correct alternative :

If `int_0^"a" 3x^2*dx` = 8, then a = ?


Fill in the blank : `int_4^9 (1)/sqrt(x)*dx` = _______


State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_"a"^"b" f("t")*dt`


State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_"a"^"b" f(x - "a" - "b")*dx`


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


Solve the following : `int_2^4 x/(x^2 + 1)*dx`


`int_1^2 ("e"^(1/x))/(x^2)  "d"x` =


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


Prove that: `int_0^"a" "f"(x)  "d"x = int_0^"a" "f"("a" - x)  "d"x`. Hence find `int_0^(pi/2) sin^2x  "d"x` 


Choose the correct alternative:

`int_2^3 x^4  "d"x` =


State whether the following statement is True or False:

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


Evaluate `int_1^"e" 1/(x(1 + log x)^2)  "d"x`


Evaluate `int_2^3 x/((x + 2)(x + 3))  "d"x`


Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2))  "d"x`


`int_((-pi)/8)^(pi/8) log ((2 - sin x)/(2 + sin x))` dx = ______.


`int_(-2)^2 sqrt((2 - x)/(2 + x))` = ?


`int_0^(pi/2) (cos x)/((4 + sin x)(3 + sin x))`dx = ?


`int_(-5)^5 log ((7 - x)/(7 + x))`dx = ?


`int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2))` dx = ?


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


`int_2^3 "x"/("x"^2 - 1)` dx = ____________.


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


Evaluate the following definite intergral:

`int_4^9 1/sqrt(x)dx`


Evaluate the following definite integral:

`int_1^3 log x  dx`


Solve the following.

`int_1^3 x^2 logx  dx`


Evaluate the following definite intergral:

`int_1^3 log xdx`


Evaluate the following definite intergral:

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


Solve the following.

`int_1^3x^2 logx dx`


`int_0^(π/2) (sin^2 x.dx)/(1 + cosx)^2` = ______.


Evaluate:

`int_0^1 |x| dx`


Evaluate the following definite intergral:

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


Solve the following.

`int_1^3 x^2 log x dx `


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


The principle solutions of the equation cos θ = `1/2` are ______.


Evaluate the following definite integral:

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


Evaluate the following definite intergral:

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


Evaluate the following definite intergral:

`int_4^9 1/sqrtx dx`


Evaluate the following definite intergral:

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


Evaluate the following integral:

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


Share
Notifications



      Forgot password?
Use app×