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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

If f(x) = gsin-1x1-x2,g(x)=esin-1x, then g∫f(x)⋅g(x)⋅dx = ______. - Mathematics and Statistics

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प्रश्न

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.

पर्याय

  • `e^(sin^-1x)*(sin^-1 x - 1) + c`

  • `e^(sin^-1x)*(1 - sin^-1x) + c`

  • `e^(sin^-1x)*(sin^-1 x + 1) + c`

  • `-e^(sin^-1x)*(sin^-1 x + 1) + c`

MCQ
रिकाम्या जागा भरा

उत्तर

If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = `underlinebb(e^(sin^-1x)*(sin^-1 x - 1) + c)`.

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पाठ 2.3: Indefinite Integration - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

`int1/xlogxdx=...............`

(A)log(log x)+ c

(B) 1/2 (logx )2+c

(C) 2log x + c

(D) log x + c


Integrate the function in x sin x.


Integrate the function in xlog x.


Integrate the function in x tan-1 x.


Integrate the function in x cos-1 x.


Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.


Integrate the function in x sec2 x.


Integrate the function in x (log x)2.


Integrate the function in `((x- 3)e^x)/(x - 1)^3`.


Prove that:

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


Evaluate the following : `int x.sin^2x.dx`


Evaluate the following : `int x^3.logx.dx`


Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`


Evaluate the following : `int sin θ.log (cos θ).dθ`


Evaluate the following : `int cos(root(3)(x)).dx`


Integrate the following functions w.r.t. x : `sqrt(x^2 + 2x + 5)`


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


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


Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)] 


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives :

`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =


Choose the correct options from the given alternatives :

`int [sin (log x) + cos (log x)]*dx` =


Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`


Evaluate the following.

`int "x"^2 "e"^"3x"`dx


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


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


Choose the correct alternative from the following.

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


Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 


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


Evaluate: `int "dx"/("9x"^2 - 25)`


Evaluate: `int "dx"/(5 - 16"x"^2)`


`int 1/(4x + 5x^(-11))  "d"x`


`int ["cosec"(logx)][1 - cot(logx)]  "d"x`


`int sin4x cos3x  "d"x`


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


Evaluate `int 1/(x log x)  "d"x`


`int logx/(1 + logx)^2  "d"x`


`int 1/sqrt(x^2 - 8x - 20)  "d"x`


∫ log x · (log x + 2) dx = ?


`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.


The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.


The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1)  dx` is


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


Find: `int e^x.sin2xdx`


Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.


Solve: `int sqrt(4x^2 + 5)dx`


If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.


`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.


Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.


Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.


`int(1-x)^-2 dx` = ______


`intsqrt(1+x)  dx` = ______


`int1/(x+sqrt(x))  dx` = ______


`int logx  dx = x(1+logx)+c`


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


The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.


Evaluate `int tan^-1x  dx`


If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv  dx - int(d/dx u)(intv  dx)dx`. Hence evaluate: `intx cos x  dx`


Evaluate the following.

`intx^3  e^(x^2) dx`


Complete the following activity:

`int_0^2 dx/(4 + x - x^2) `

= `int_0^2 dx/(-x^2 + square + square)`

= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`

= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`

= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`


Evaluate:

`int1/(x^2 + 25)dx`


Evaluate the following:

`intx^3e^(x^2)dx` 


Evaluate the following.

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


Evaluate the following.

`intx^3/sqrt(1+x^4)  dx`


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


Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  


Evaluate the following.

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


Evaluate the following.

`intx^2e^(4x)dx`


The value of `inta^x.e^x dx` equals


Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`


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