English

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

Advertisements
Advertisements

Question

Choose the correct options from the given alternatives :

`int [sin (log x) + cos (log x)]*dx` =

Options

  • x cos (log x) + c

  • sin (log x) + c

  • cos (log x) + c

  • x sin (log x) + c

MCQ
Advertisements

Solution

x sin (log x) + c

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 150]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.18 | Page 150

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


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


Integrate the function in x log 2x.


Integrate the function in x (log x)2.


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


Evaluate the following : `int e^(2x).cos 3x.dx`


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


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


Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`


Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]e 


Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`


Choose the correct options from the given alternatives :

`int (x- sinx)/(1 - cosx)*dx` =


Choose the correct options from the given alternatives :

`int sin (log x)*dx` =


Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`


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


Integrate the following w.r.t.x : cot–1 (1 – x + x2)


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


Integrate the following w.r.t.x : e2x sin x cos x


Evaluate the following.

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


Choose the correct alternative from the following.

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


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


`int (cos2x)/(sin^2x cos^2x)  "d"x`


`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`


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


`int log x * [log ("e"x)]^-2` dx = ?


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


Evaluate the following:

`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`


Evaluate the following:

`int_0^pi x log sin x "d"x`


`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.


Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`


Solve: `int sqrt(4x^2 + 5)dx`


If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.


`int1/(x+sqrt(x))  dx` = ______


Evaluate `int(3x-2)/((x+1)^2(x+3))  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`


Evaluate:

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


Evaluate:

`inte^x sinx  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 tan^-1x  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:

`int x^2 cos x  dx`


Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  


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


Evaluate the following.

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


Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×