English

∫cosx dx = _____________ - Mathematics and Statistics

Advertisements
Advertisements

Question

`int cos sqrtx` dx = _____________

Options

  • `2 [sqrtx sin sqrtx + cos sqrtx] + "c"`

  • `sqrtx sin sqrtx + cos sqrtx + "c"`

  • `2 [sqrtx cos sqrtx + sin sqrtx] + "c"`

  • `1/2 [sqrtx sin sqrtx - cos sqrtx] + "c"`

MCQ
Fill in the Blanks

Solution

`2 [sqrtx sin sqrtx + cos sqrtx] + "c"`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.3: Indefinite Integration - MCQ

RELATED QUESTIONS

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


Evaluate :

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


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


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


Integrate the functions:

`1/(x-sqrtx)`


Integrate the functions:

`x/(9 - 4x^2)`


Integrate the functions:

`sin x/(1+ cos x)`


Integrate the functions:

`1/(1 + cot x)`


Integrate the functions:

`1/(1 - tan x)`


Solve: dy/dx = cos(x + y)


\[\int\sqrt{1 + x - 2 x^2} \text{ dx }\]

\[\int e^x \sqrt{e^{2x} + 1} \text{ dx}\]

\[\int\sqrt{4 x^2 - 5}\text{ dx}\]

Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]


Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]


\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]


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


Integrate the following w.r.t. x:

`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`


Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`


Evaluate the following integrals : `int sinx/(1 + sinx)dx`


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


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


Integrate the following functions w.r.t. x : sin4x.cos3x


Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`


Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`


Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`


Integrate the following functions w.r.t. x : cos7x


Integrate the following functions w.r.t. x : sin5x.cos8x


Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`


Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`


Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`


Evaluate the following:

`int (1)/sqrt((x - 3)(x + 2)).dx`


Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`


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


Evaluate the following integrals : `int (3cosx)/(4sin^2x + 4sinx - 1).dx`


Evaluate `int (3"x"^2 - 5)^2` dx


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


Evaluate the following.

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


Evaluate the following.

`int 1/(4"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 1/("a"^2 - "b"^2 "x"^2)` dx


Fill in the Blank.

To find the value of `int ((1 + log "x") "dx")/"x"` the proper substitution is ________


Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).


Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx


`int x^2/sqrt(1 - x^6)` dx = ________________


`int 2/(sqrtx - sqrt(x + 3))` dx = ________________


`int logx/x  "d"x`


`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1))  "d"x`


State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`


`int (1 + x)/(x + "e"^(-x))  "d"x`


`int sin^-1 x`dx = ?


If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 


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


`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.


`int (f^'(x))/(f(x))dx` = ______ + c.


`int(7x - 2)^2dx = (7x -2)^3/21 + c`


If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.


If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.


`int (x + sinx)/(1 + cosx)dx` is equal to ______.


The value of `sqrt(2) int (sinx  dx)/(sin(x - π/4))` is ______.


Find `int dx/sqrt(sin^3x cos(x - α))`.


Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.


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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int x sqrt(1 + x^2)  dx`


Evaluate the following

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


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


Evaluate the following.

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


Evaluate the following.

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


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


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


Evaluate:

`intsqrt(sec  x/2 - 1)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×