State whether the following statement is True or False: ∫1+x2⋅xdx=13(1+x2)32+c - Mathematics and Statistics

Advertisements
Advertisements
MCQ
True or False

State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`

Options

  • True

  • False

Advertisements

Solution

True

  Is there an error in this question or solution?
Chapter 1.5: Integration - Q.3

RELATED QUESTIONS

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`


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


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Find : `int(x+3)sqrt(3-4x-x^2dx)`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.


Evaluate :   `∫1/(cos^4x+sin^4x)dx`


 
 

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

 
 

Integrate the functions:

`x^2/(2+ 3x^3)^3`


Integrate the functions `(e^(2x) -  e^(-2x))/(e^(2x) + e^(-2x))`


Integrate the functions `(2cosx - 3sinx)/(6cos x + 4 sin x)`


Integrate the functions `1/(cos^23 x(1- tan x)^2`


Integrate the functions `cos x /(sqrt(1+sinx))`


Integrate the functions `sin x/(1+ cos x)`


Integrate the functions in `1/(1 + cot x)`


Integrate the functions in `((x+1)(x + logx)^2)/x`


Integrate the functions in `(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


Evaluate : `∫1/(3+2sinx+cosx)dx`


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


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


Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`


Evaluate: `int (2y^2)/(y^2 + 4)dx`


Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`


Evaluate: `int (sec x)/(1 + cosec x) dx`


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

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

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

\[\int\sqrt{16 x^2 + 25} \text{ dx}\]

Write a value of

\[\int e^x \sec x \left( 1 + \tan x \right) \text{ dx }\]

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]


Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]


Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]


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


Write a value of\[\int\frac{\cos x}{\sin x \log \sin x} dx\]

 


Write a value of\[\int e^{ax} \sin\ bx\ dx\]


Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .


Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .


Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]


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

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is


\[\int\frac{\cos^5 x}{\sin x} \text{ dx }\]

\[\int x \sin^3 x\ dx\]

Integrate the following w.r.t. x : x3 + x2 – x + 1


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


Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`


Evaluate the following integrals : `int sin x/cos^2x dx`


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


Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`


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


Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`


If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)


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


Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`


Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`


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 : `(e^(2x) + 1)/(e^(2x) - 1)`


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


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


Integrate the following functions w.r.t. x : `(10x^9  10^x.log10)/(10^x + x^10)`


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


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


Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`


Integrate the following functions w.r.t. x : `cosx/sin(x - a)`


Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`


Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`


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


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


Integrate the following functions w.r.t. x : tan5x


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


Evaluate the following : `int (1)/(25 - 9x^2).dx`


Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`


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


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


Evaluate the following : `(1)/(4x^2 - 20x + 17)`


Evaluate the following:

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


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


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


Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`


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


Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`


Evaluate the following integrals:

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


Evaluate the following integrals:

`int (7x + 3)/sqrt(3 + 2x - x^2).dx`


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


Choose the correct options from the given alternatives :

`int sqrt(cotx)/(sinx*cosx)*dx` =


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives :

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


`int logx/(log ex)^2*dx` = ______.


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`


integrate the following with respect to the respective variable : `x^2/(x + 1)`


If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).


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


Evaluate the following.

`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx


Evaluate the following.

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


Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is


State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t


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


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


Evaluate: `int "e"^sqrt"x"` dx


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


`int (sin4x)/(cos 2x) "d"x`


`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`


`int (cos2x)/(sin^2x)  "d"x`


`int cos^7 x  "d"x`


`int(log(logx))/x  "d"x`


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


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


State whether the following statement is True or False:

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


Evaluate `int(3x^2 - 5)^2  "d"x`


`int sin^-1 x`dx = ?


`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?


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


`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.


`int (cos x)/(1 - sin x) "dx" =` ______.


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


`int sec^6 x tan x   "d"x` = ______.


If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.


If f'(x) = `x + 1/x`, then f(x) is ______.


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 ______.


`int (sin  (5x)/2)/(sin  x/2)dx` is equal to ______. (where C is a constant of integration).


`int(log(logx) + 1/(logx)^2)dx` = ______.


`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.


The value of `intsinx/(sinx - cosx)dx` equals ______.


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 ______.


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


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


`int cos^3x  dx` = ______.


Write `int cotx  dx`.


`int (logx)^2/x dx` = ______.


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


Evaluate the following

`int1/(x^2 +4x-5)dx`


Evaluate.

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


Evaluate the following.

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


`int dx/((x+2)(x^2 + 1))`    ...(given)

`1/(x^2 +1) dx = tan ^-1 + c`


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


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate the following

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


Evaluate:

`int sqrt((a - x)/x) dx`


Evaluate:

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


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


`int "cosec"^4x  dx` = ______.


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


Evaluate the following.

`int1/(x^2+4x-5) dx`


`int 1/(sin^2x cos^2x)dx` = ______.


Evaluate:

`intsqrt(3 + 4x - 4x^2)  dx`


The value of `int dx/(sqrt(1 - x))` is ______.


Evaluate the following:

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


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


Evaluate the following.

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


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


Evaluate the following.

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


Share
Notifications



      Forgot password?
Use app×