मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

∫1cosx-sinx dx = _______________

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प्रश्न

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

पर्याय

  • `1/sqrt2 log ["cosec" (x + π/4) - cot (x + π/4)] + "c"`

  • `sqrt2 log ["cosec" (x + π/4) + cot (x + π/4)] + "c"`

  • `1/sqrt2 log [sec (x + π/4) + tan (x + π/4)] + "c"`

  • `sqrt2 log [sec (x + π/4) - tan (x + π/4)] + "c"`

MCQ
रिकाम्या जागा भरा
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उत्तर

`1/sqrt2 log [sec (x + π/4) + tan (x + π/4)] + "c"`

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`


Integrate the functions:

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


Integrate the functions:

tan2(2x – 3)


Integrate the functions:

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


Integrate the functions:

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


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

Write a value of

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

 


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


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

 


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


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

 

 


Find : ` int  (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`


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


Evaluate the following integral: 

`int(4x + 3)/(2x + 1).dx`


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


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


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


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


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


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


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


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


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


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


Evaluate the following.

∫ (x + 1)(x + 2)7 (x + 3)dx


Evaluate the following.

`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt


Evaluate the following.

`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx


Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx


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


Evaluate: `int 1/(2"x" + 3"x" log"x")` dx


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


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


`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________


`int ("e"^(3x))/("e"^(3x) + 1)  "d"x`


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"`


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


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


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


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


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


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


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


Evaluate the following.

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


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


What is integration by substitution?


What is the value of \[\int\sin^3x\cos^2x\,dx\]?


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