English

Integrate the function in x sin x. - Mathematics

Advertisements
Advertisements

Question

Integrate the function in x sin x.

Sum

Solution

Let `I = int x  sin x  dx`

`= x int sin x  dx - int [d/dx  (x) int sin x  dx] dx`

[Integration by Parts]

`= x (- cos x) - int 1 (- cos x) dx`

`= - x cos x + int cos x  dx`

`= - x cos x + sin x + C`

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.6 [Page 327]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 7 Integrals
Exercise 7.6 | Q 1 | Page 327

RELATED QUESTIONS

If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:

(A) 0

(B) π

(C) π/2

(D) π/4


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


Integrate the function in tan-1 x.


Integrate the function in ex (sinx + cosx).


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


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


Evaluate the following : `int e^(2x).cos 3x.dx`


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


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


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


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


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


Choose the correct options from the given alternatives :

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


Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`


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


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


Evaluate the following.

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


Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx


`int sin4x cos3x  "d"x`


Choose the correct alternative:

`int ("d"x)/((x - 8)(x + 7))` =


`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + ______ + c


State whether the following statement is True or False:

If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1|  + B log|x – 2|, then A + B = 1


Evaluate `int 1/(4x^2 - 1)  "d"x`


`int logx/(1 + logx)^2  "d"x`


`int log x * [log ("e"x)]^-2` dx = ?


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


Evaluate the following:

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


Evaluate the following:

`int_0^pi x log sin x "d"x`


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


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


Evaluate:

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


Evaluate:

`inte^x sinx  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 ______.


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 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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×