मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Evaluate ∫14x2-1 dx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Evaluate `int 1/(4x^2 - 1)  "d"x`

बेरीज
Advertisements

उत्तर

Let I = `int ("d"x)/(4x^2 - 1)`

= `1/4 int ("d"x)/(x^2 - 1/4)`

= `1/4 int ("d"x)/(x^2 - (1/2)^2`

= `1/4 xx 1/(2 xx 1/2) log |(x - 1/2)/(x + 1/2)| + "c"`

∴ I = `1/4 log|(2x - 1)/(2x + 1)| + "c"`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.5: Integration - Q.4

संबंधित प्रश्‍न

If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:

(A) 0

(B) π

(C) π/2

(D) π/4


If u and v are two functions of x then prove that

`intuvdx=uintvdx-int[du/dxintvdx]dx`

Hence evaluate, `int xe^xdx`


Integrate the function in x log x.


`intx^2 e^(x^3) dx` equals: 


Find : 

`∫(log x)^2 dx`


Evaluate the following:

`int x tan^-1 x . dx`


Evaluate the following: `int x.sin^-1 x.dx`


Evaluate the following : `int cos sqrt(x).dx`


Integrate the following functions w.r.t.x:

`e^-x cos2x`


Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`


Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.


Choose the correct options from the given alternatives :

`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =


If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.


Integrate the following with respect to the respective variable : cos 3x cos 2x cos x


Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`


Evaluate: `int "dx"/("9x"^2 - 25)`


Evaluate: `int "dx"/(5 - 16"x"^2)`


`int 1/sqrt(2x^2 - 5)  "d"x`


`int sqrt(tanx) + sqrt(cotx)  "d"x`


`int ("d"x)/(x - x^2)` = ______


Evaluate `int 1/(x(x - 1))  "d"x`


If u and v ore differentiable functions of x. then prove that:

`int uv  dx = u intv  dx - int [(du)/(d) intv  dx]dx`

Hence evaluate `intlog x  dx`


`int 1/sqrt(x^2 - 9) dx` = ______.


`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`


`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.


Evaluate the following.

`int x^3 e^(x^2) dx`


Evaluate:

`int e^(ax)*cos(bx + c)dx`


Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`


Evaluate:

`int (sin(x - a))/(sin(x + a))dx`


If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv  dx - int(d/dx u)(intv  dx)dx`. Hence evaluate: `intx cos x  dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×