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Choose the correct options from the given alternatives : ∫tan(sin-1x)⋅dx =

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प्रश्न

Choose the correct options from the given alternatives :

`int tan(sin^-1 x)*dx` =

पर्याय

  • `(1 - x^2)^(-1/2) + c`

  • `(1 - x^2)^(1/2) + c`

  • `tan^m x/sqrt(1 - x^2) + c`

  • `- sqrt(1 - x^2) + c`

MCQ
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उत्तर

`-sqrt(1 - x^2) + c`

`["Hint" : sin^-1x = tan^-1 (x/sqrt(1 - x^2))].`

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पाठ 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १४८]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.05 | पृष्ठ १४८

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 cos^(-1) x)/sqrt(1-x^2)`.


Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.


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


Evaluate the following: `int x.sin^-1 x.dx`


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


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

`e^-x cos2x`


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


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


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

`e^(5x).[(5x.logx + 1)/x]`


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


Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`


Integrate the following w.r.t.x : cot–1 (1 – x + x2)


Integrate the following w.r.t.x : e2x sin x cos x


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

`int [1/(log "x") - 1/(log "x")^2]` dx


Evaluate the following.

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


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


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


`int (sinx)/(1 + sin x)  "d"x`


`int sqrt(tanx) + sqrt(cotx)  "d"x`


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


`int"e"^(4x - 3) "d"x` = ______ + c


`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?


`int tan^-1 sqrt(x)  "d"x` is equal to ______.


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


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


`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.


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


Evaluate the following.

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


Solve the differential equation (x2 + y2) dx - 2xy dy = 0 by completing the following activity.

Solution: (x2 + y2) dx - 2xy dy = 0

∴ `dy/dx=(x^2+y^2)/(2xy)`                      ...(1)

Puty = vx

∴ `dy/dx=square`

∴ equation (1) becomes

`x(dv)/dx = square`

∴ `square  dv = dx/x`

On integrating, we get

`int(2v)/(1-v^2) dv =intdx/x`

∴ `-log|1-v^2|=log|x|+c_1`

∴ `log|x| + log|1-v^2|=logc       ...["where" - c_1 = log c]`

∴ x(1 - v2) = c

By putting the value of v, the general solution of the D.E. is `square`= cx


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


Evaluate:

`int((1 + sinx)/(1 + cosx))e^x dx`


`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.


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`


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


Evaluate the following.

`intx^3  e^(x^2) dx`


Evaluate the following:

`intx^3e^(x^2)dx` 


Evaluate the following.

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


Evaluate the following.

`intx^3/sqrt(1+x^4)  dx`


Evaluate the following.

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


If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.


Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  


Evaluate the following.

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


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