English

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

Advertisements
Advertisements

Question

Choose the correct options from the given alternatives :

`int (sin^m x)/(cos^(m+2)x)*dx` = 

Options

  • `(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

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 148]

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Integrate : sec3 x w. r. t. x.


Integrate the function in x log x.


Integrate the function in x sec2 x.


Integrate the function in (x2 + 1) log x.


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


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


Evaluate the following:

`int x^2 sin 3x  dx`


Evaluate the following:

`int x tan^-1 x . dx`


Evaluate the following : `int x^3.tan^-1x.dx`


Evaluate the following : `int log(logx)/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 : `e^x/x [x (logx)^2 + 2 (logx)]`


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


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


Choose the correct options from the given alternatives :

`int sin (log x)*dx` =


Choose the correct options from the given alternatives :

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


Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`


Solve the following differential equation.

(x2 − yx2 ) dy + (y2 + xy2) dx = 0


Evaluate the following.

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


Evaluate the following.

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


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


Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 


Evaluate: Find the primitive of `1/(1 + "e"^"x")`


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


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


`int (sinx)/(1 + sin x)  "d"x`


`int "e"^x x/(x + 1)^2  "d"x`


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


Evaluate the following:

`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`


Evaluate the following:

`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`


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


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


`int_0^1 x tan^-1 x  dx` = ______.


`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`


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:

`intcos^-1(sqrt(x))dx`


Evaluate:

`int e^(logcosx)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`


Evaluate the following.

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


Evaluate the following.

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


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


Evaluate the following.

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


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


Which expression is the integration-by-parts form for a product \(f(x)g(x)\)?


For the special integral \[\int e^x\left[f(x)+f'(x)\right]dx,\] what is the antiderivative?


When applying integration by parts to \(\log x\) and inverse trig, what should they be multiplied by?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×