हिंदी

Choose the correct options from the given alternatives : ∫sin(logx)⋅dx = - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct options from the given alternatives :

`int sin (log x)*dx` =

विकल्प

  • `x/(2)[sin (log x) - cos (log x)] + c`

  • `x/(2)[sin (log x) + cos (log x)] + c`

  • `x/(2)[cos (log x) - sin (log x)] + c`

  • `x/(4)[cos (log x) - sin (log x)] + c`

MCQ

उत्तर

`x/(2)[sin (log x) - cos (log x)] + c`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १४९]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.12 | पृष्ठ १४९

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Prove that:

`int sqrt(a^2 - x^2) dx = x/2 sqrt(a^2 - x^2) + a^2/2sin^-1(x/a)+c`


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


`int1/xlogxdx=...............`

(A)log(log x)+ c

(B) 1/2 (logx )2+c

(C) 2log x + c

(D) log x + c


Integrate the function in x sin x.


Integrate the function in `x^2e^x`.


Integrate the function in x log x.


Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.


Integrate the function in tan-1 x.


Integrate the function in (x2 + 1) log x.


Integrate the function in `e^x (1 + sin x)/(1+cos x)`.


Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.


Evaluate the following:

`int sec^3x.dx`


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


Evaluate the following:

`int x.sin 2x. cos 5x.dx`


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


Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`


Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`


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


Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`


Choose the correct options from the given alternatives :

`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =


Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`


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


Integrate the following w.r.t. x: `(1 + log x)^2/x`


Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`


Integrate the following w.r.t.x : log (log x)+(log x)–2 


Evaluate the following.

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


Evaluate the following.

`int "e"^"x" "x"/("x + 1")^2` dx


Evaluate the following.

`int [1/(log "x") - 1/(log "x")^2]` dx


Evaluate the following.

`int (log "x")/(1 + log "x")^2` dx


Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 


Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx


Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`


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


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


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


Evaluate: ∫ (log x)2 dx


`int (sinx)/(1 + sin x)  "d"x`


`int 1/sqrt(2x^2 - 5)  "d"x`


`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + ______ + c


Evaluate `int (2x + 1)/((x + 1)(x - 2))  "d"x`


`int 1/sqrt(x^2 - 8x - 20)  "d"x`


∫ log x · (log x + 2) dx = ?


`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.


`int cot "x".log [log (sin "x")] "dx"` = ____________.


The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.


Evaluate the following:

`int_0^pi x log sin x "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`


Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`


If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.


`int_0^1 x tan^-1 x  dx` = ______.


`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.


Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.


Find: `int e^(x^2) (x^5 + 2x^3)dx`.


`intsqrt(1+x)  dx` = ______


Evaluate: 

`int(1+logx)/(x(3+logx)(2+3logx))  dx`


Solve the differential equation (x2 + y2) dx - 2xy dy = 0 by completing the following activity.

Solution: (x2 + y2) dx - 2xy dy = 0

∴ `dy/dx=(x^2+y^2)/(2xy)`                      ...(1)

Puty = vx

∴ `dy/dx=square`

∴ equation (1) becomes

`x(dv)/dx = square`

∴ `square  dv = dx/x`

On integrating, we get

`int(2v)/(1-v^2) dv =intdx/x`

∴ `-log|1-v^2|=log|x|+c_1`

∴ `log|x| + log|1-v^2|=logc       ...["where" - c_1 = log c]`

∴ x(1 - v2) = c

By putting the value of v, the general solution of the D.E. is `square`= cx


Evaluate `int(1 + x + (x^2)/(2!))dx`


Evaluate the following.

`int (x^3)/(sqrt(1 + x^4))dx`


Solve the following

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


Evaluate:

`int e^(logcosx)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`


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`


Evaluate the following.

`intx^3/sqrt(1+x^4)dx`


Evaluate the following.

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


Evaluate the following.

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


If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Evaluate the following.

`int x^3 e^(x^2) dx` 


The value of `inta^x.e^x dx` equals


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×