Karnataka Board PUCPUC Science 2nd PUC Class 12

Write a Value of ∫ √ 9 + X 2 D X - Mathematics

Advertisements
Advertisements
Sum

Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].

Advertisements

Solution

\[\int \sqrt{9 + x^2} \text{ dx }\]
\[ = \int \sqrt{3^2 + x^2} dx \left( \because \sqrt{a^2 + x^2} = \frac{x}{2}\sqrt{x^2 + a^2} + \frac{a^2}{2}\text{ ln }\left| x + \sqrt{x^2 + a^2} \right| \right)\]
\[ = \frac{x}{2}\sqrt{9 + x^2} + \frac{9}{2}\text{ ln }\left| x + \sqrt{9 + x^2} \right| + C\]

  Is there an error in this question or solution?
Chapter 19: Indefinite Integrals - Very Short Answers [Page 198]

APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 36 | Page 198

RELATED QUESTIONS

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


Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^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 `intsqrtx/sqrt(a^3-x^3)dx`


Evaluate :   `∫1/(cos^4x+sin^4x)dx`


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


Integrate the functions:

`(log x)^2/x`


Integrate the functions:

sin x ⋅ sin (cos x)


Integrate the functions:

sin (ax + b) cos (ax + b)


Integrate the functions:

`1/(x-sqrtx)`


Integrate the functions:

`x/(sqrt(x+ 4))`, x > 0 


Integrate the functions:

`1/(x(log x)^m),  x > 0, m ne 1`


Integrate the functions:

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


Integrate the functions:

`1/(cos^2 x(1-tan x)^2`


Integrate the functions:

`cos x /(sqrt(1+sinx))`


Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


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


Evaluate `int 1/(3+ 2 sinx + cosx) 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`


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

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

\[\int\sqrt{9 - x^2}\text{ dx}\]

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

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

\[\int\frac{\cos x}{3 + 2 \sin x}\text{  dx}\]

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]

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


Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


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


Write a value of

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

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


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

The value of \[\int\frac{1}{x + x \log x} dx\] is


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

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

`int "dx"/(9"x"^2 + 1)= ______. `


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


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


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


Evaluate the following integrals:

`int x/(x + 2).dx`


Evaluate the following integrals:

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


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


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


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


Integrate the following functions w.r.t. x : x9.sec2(x10)


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:

`(2sinx cosx)/(3cos^2x + 4sin^2 x)`


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


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


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 : `sin(x - a)/cos(x  + b)`


Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`


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


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


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 (1)/(5 - 4x - 3x^2).dx`


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


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


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


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


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


Evaluate the following integrals:

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


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


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


Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*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 : 

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


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


Evaluate the following.

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


Evaluate the following.

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


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


Choose the correct alternative from the following.

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


Choose the correct alternative from the following.

`int "dx"/(("x" - "x"^2))`= 


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: `int "e"^sqrt"x"` dx


`int 1/(cos x - sin x)` dx = _______________


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


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


`int (log x)/(log ex)^2` dx = _________


`int sqrt(1 + sin2x)  "d"x`


`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`


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


`int x^x (1 + logx)  "d"x`


`int (cos2x)/(sin^2x)  "d"x`


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


`int (1 + x)/(x + "e"^(-x))  "d"x`


If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.


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


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


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


If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


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


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 ______.


The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.


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


`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)


`int cos^3x  dx` = ______.


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


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


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


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


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


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate.

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


Evaluate the following

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


Evaluate:

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


`int "cosec"^4x  dx` = ______.


Evaluate:

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


Evaluate.

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


Evaluate the following.

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


Evaluate the following.

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


Evaluate:

`int(cos 2x)/sinx dx`


`int (cos4x)/(sin2x + cos2x)dx` = ______.


Evaluate:

`int sin^3x cos^3x  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 `int(1+x+x^2/(2!))dx`


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


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


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


Evaluate the following.

`int1/(x^2 + 4x - 5)  dx`


Share
Notifications



      Forgot password?
Use app×