हिंदी

Choose the correct alternative: ∫x23x3dx =

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

`intx^(2)3^(x^3) "d"x` =

विकल्प

  • `(3)^(x^3) + "c"`

  • `((3)^(x^3))/(3log3) + "c"`

  • `log 3*(3)^(x^3) + "c"`

  • `x^2 (3)^(x^2) + "c"`

MCQ
Advertisements

उत्तर

`((3)^(x^3))/(3log3) + "c"` 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.5: Integration - Q.1

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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


Integrate the function in `x^2e^x`.


Integrate the function in x sin−1 x.


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


Integrate the function in `e^x (1 + sin x)/(1+cos x)`.


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 e^(2x).cos 3x.dx`


Integrate the following functions w.r.t. x : `e^(2x).sin3x`


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


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


Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`


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


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


`int sqrt(tanx) + sqrt(cotx)  "d"x`


`int cot "x".log [log (sin "x")] "dx"` = ____________.


Find `int_0^1 x(tan^-1x)  "d"x`


`int(logx)^2dx` equals ______.


If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.


If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.


`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 e^x ((1 - sinx)/(1 - cosx))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 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`


Integration by parts is a method of integration based on which rule of differentiation?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×