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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫x21-x6 dx = ________________ - Mathematics and Statistics

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प्रश्न

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

पर्याय

  • −sin−1 (x3) + c

  • cos−1 (x3) + c

  • sin−1 (x3) + c

  • `1/3 sin^(-1) (x^3) + "c"`

MCQ
रिकाम्या जागा भरा

उत्तर

`1/3 sin^(-1) (x^3) + "c"`

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Integrate the functions:

`(x^3 - 1)^(1/3) x^5`


Integrate the functions:

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


Integrate the functions:

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


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


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

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

Write a value of\[\int \log_e x\ dx\].

 


Write a value of

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

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

 


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


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


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


Evaluate the following integrals : tan2x dx


Evaluate the following integrals : `int (sin2x)/(cosx)dx`


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


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


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


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


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


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


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


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

cos8xcotx


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


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


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


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


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


Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 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 dx/(cosxsqrt(sin^2x - cos^2x))*dx` =


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


Choose the correct options from the given alternatives :

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


Evaluate the following.

`int 1/(sqrt"x" + "x")` dx


Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx


`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c


Fill in the Blank.

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


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


Evaluate: ∫ |x| dx if x < 0


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


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


Evaluate: `int log ("x"^2 + "x")` dx


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


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


`int 1/(xsin^2(logx))  "d"x`


`int cot^2x  "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)`


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


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


`int1/(4 + 3cos^2x)dx` = ______ 


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


`int(sin2x)/(5sin^2x+3cos^2x)  dx=` ______.


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


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


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


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


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


`int dx/(2 + cos x)` = ______.

(where C is a constant of integration)


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


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


Evaluate.

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


Evaluate the following.

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


Prove that:

`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.


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


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


Evaluate:

`int(cos 2x)/sinx dx`


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


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


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


Evaluate the following.

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


Evaluate the following.

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


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