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

Choose the correct options from the given alternatives : ∫sinmxcosm+2x⋅dx =

Advertisements
Advertisements

प्रश्न

Choose the correct options from the given alternatives :

`int (sin^m x)/(cos^(m+2)x)*dx` = 

पर्याय

  • `(tan^(m+1)x)/(m + 1) + c`

  • (m + 2)tanm+1 x + c

  • `tan^mx/m + c`

  • (m + 1)tanm+1 x + c

MCQ
Advertisements

उत्तर

`(tan^(m+1)x)/(m + 1) + c`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Indefinite Integration - Miscellaneous Exercise 3 [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 log 2x.


Integrate the function in x2 log x.


Integrate the function in x tan-1 x.


`int e^x sec x (1 +   tan x) dx` equals:


Evaluate the following : `int x^2*cos^-1 x*dx`


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


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


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

`e^-x cos2x`


Integrate the following functions w.r.t. x : `x^2 .sqrt(a^2 - x^6)`


Integrate the following functions w.r.t. x : `sqrt(2x^2 + 3x + 4)`


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


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


Choose the correct options from the given alternatives :

`int (x- sinx)/(1 - cosx)*dx` =


Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`


Evaluate the following.

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


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


Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx


Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`


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


`int 1/(4x + 5x^(-11))  "d"x`


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


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


∫ log x · (log x + 2) dx = ?


`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.


`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.


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


`int 1/sqrt(x^2 - 9) dx` = ______.


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


`intsqrt(1+x)  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


`inte^(xloga).e^x dx` is ______


`int logx  dx = x(1+logx)+c`


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`


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/sqrt(1+x^4)  dx`


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


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


Evaluate:

`int x^2 cos x  dx`


Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  


Which function is an example under priority \(I\) in the LIATE rule?


Evaluate \[\int e^x\sin x\,dx.\]


Repeated parts may be needed for which pair of integrals?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×