State whether the following statement is True or False: ∫32x+3 dx=32x+32+c - Mathematics and Statistics

Advertisements
Advertisements
MCQ
True or False

State whether the following statement is True or False:

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

Options

  • True

  • False

Advertisements

Solution

False

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

RELATED QUESTIONS

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`


Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Find : `int((2x-5)e^(2x))/(2x-3)^3dx`


Find : `int(x+3)sqrt(3-4x-x^2dx)`


Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Evaluate :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Integrate the functions:

`(2x)/(1 + x^2)`


Integrate the functions:

`(log x)^2/x`


Integrate the functions:

(4x + 2) `sqrt(x^2 + x +1)`


Integrate the functions:

`x/(sqrt(x+ 4))`, x > 0 


Integrate the functions:

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


Integrate the functions:

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


Integrate the functions:

sec2(7 – 4x)


Integrate the functions:

`sqrt(sin 2x) cos 2x`


Integrate the functions:

`1/(1 - tan x)`


Integrate the functions:

`(1+ log x)^2/x`


`int (dx)/(sin^2 x cos^2 x)` equals:


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


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`


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

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

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

Write a value of

\[\int x^2 \sin x^3 \text{ dx }\]

Write a value of

\[\int \tan^3 x \sec^2 x \text{ dx }\].

 


Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 


Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

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


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


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

 


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


Write a value of

\[\int\frac{a^x}{3 + a^x} \text{ dx}\]

Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

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


Evaluate:  \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]


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

 

 


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

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


 Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`


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


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


Evaluate the following integrals : `int tanx/(sec x + tan x)dx`


Evaluate the following integrals:

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


Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`


Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`


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 : e3logx(x4 + 1)–1 


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


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


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


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


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


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


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


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


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


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


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


Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`


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


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


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


Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`


Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`


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


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


Evaluate the following:

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


Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`


Evaluate the following : `int sinx/(sin 3x).dx`


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


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


Evaluate the following integrals:

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


Choose the correct options from the given alternatives : 

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


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


Choose the correct options from the given alternatives :

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


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


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


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


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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int 1/("x"("x"^6 + 1))` dx


Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx


Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx


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


`int sqrt(x^2 + 2x + 5)` dx = ______________


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


`int cos sqrtx` dx = _____________


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


`int 1/(xsin^2(logx))  "d"x`


`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`


`int x/(x + 2)  "d"x`


`int cos^7 x  "d"x`


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


To find the value of `int ((1 + logx))/x` dx the proper substitution is ______


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 (1 + x)/(x + "e"^(-x))  "d"x`


`int sin^-1 x`dx = ?


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


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


`int(5x + 2)/(3x - 4) dx` = ______


`int sec^6 x tan x   "d"x` = ______.


`int ("d"x)/(x(x^4 + 1))` = ______.


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


`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.


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


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


Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.


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


Evaluated the following

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


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


if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`


Solve the following Evaluate.

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


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


Evaluate the following.

`int x sqrt(1 + x^2)  dx`


`int "cosec"^4x  dx` = ______.


Evaluate:

`int sin^2(x/2)dx`


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


Evaluate the following.

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


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


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate the following.

`intxsqrt(1+x^2)dx`


Evaluate the following.

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


Evaluate the following:

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


Evaluate `int1/(x(x-1))dx` 


Evaluate:

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


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


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


Share
Notifications



      Forgot password?
Use app×