English

Choose the correct options from the given alternatives : 2∫cos2x-sin2xcos2x+sin2x⋅dx = - Mathematics and Statistics

Advertisements
Advertisements

Question

Choose the correct options from the given alternatives :

`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =

Options

  • sin 2x + c

  • cos 2x + c

  • tan 2x + c

  • 2 sin 2x + c

MCQ
Advertisements

Solution

sin 2x + c

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 149]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.15 | Page 149

RELATED QUESTIONS

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`


Evaluate : `int(x-3)sqrt(x^2+3x-18)  dx`


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Evaluate: `int sqrt(tanx)/(sinxcosx) dx`


Integrate the functions:

`sqrt(ax + b)`


Integrate the functions:

`sqrt(sin 2x) cos 2x`


Integrate the functions:

`1/(1 + cot x)`


Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


\[\int\sqrt{2 x^2 + 3x + 4} \text{ dx}\]

\[\text{ If } \int\left( \frac{x - 1}{x^2} \right) e^x dx = f\left( x \right) e^x + C, \text{ then  write  the value of  f}\left( x \right) .\]

\[If \int e^x \left( \tan x + 1 \right)\text{ sec  x  dx } = e^x f\left( x \right) + C, \text{ then  write  the value  of  f}\left( x \right) .\]

 

 


Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`


Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`


Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`


Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


Evaluate the following integrals :  `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`


Choose the correct options from the given alternatives :

`int (e^x(x - 1))/x^2*dx` =


If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).


Evaluate the following.

`int "x" sqrt(1 + "x"^2)` dx


Evaluate the following.

`int "x"^5/("x"^2 + 1)`dx


Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx


Evaluate the following.

`int 1/(4"x"^2 - 20"x" + 17)` dx


Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`


Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


Choose the correct alternative from the following.

`int "dx"/(("x" - "x"^2))`= 


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


`int 1/(xsin^2(logx))  "d"x`


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


`int dx/(1 + e^-x)` = ______


`int[ tan (log x) + sec^2 (log x)] dx= ` ______


The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.


The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.


`int cos^3x  dx` = ______.


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


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


Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`


`int "cosec"^4x  dx` = ______.


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


Evaluate the following.

`intxsqrt(1+x^2)dx`


Evaluate:

`int(5x^2-6x+3)/(2x-3)dx`


Evaluate the following.

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


Evaluate `int1/(x(x-1))dx`


Evaluate the following.

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


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


Evaluate:

`intsqrt(sec  x/2 - 1)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×