English

Integrate the functions: sin x ⋅ sin (cos x)

Advertisements
Advertisements

Question

Integrate the functions:

sin x ⋅ sin (cos x)

Sum
Advertisements

Solution

Let I `= int sin x sin  (cos x) dx`

Put cos x = t

= - sin x dx = dt

Hence, I `= - int sin t  dt`

= (cos t) + C

= cos (cos x) + C

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.2 [Page 304]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.2 | Q 4 | Page 304

RELATED QUESTIONS

Integrate the functions:

`sqrt(tanx)/(sinxcos x)`


`(10x^9 + 10^x log_e 10)/(x^10 + 10^x)  dx` equals:


Evaluate : `∫1/(3+2sinx+cosx)dx`


Evaluate: `int 1/(x(x-1)) dx`


\[\int\sqrt{x^2 + x + 1} \text{ dx}\]

 Write a valoue of \[\int \sin^3 x \cos x\ dx\]

 


Write a value of\[\int e^{ax} \sin\ bx\ dx\]


\[If \int e^x \left( \tan x + 1 \right)\text{ sec  x  dx } = e^x f\left( x \right) + C, \text{ then  write  the value  of  f}\left( x \right) .\]

 

 


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


Evaluate the following integrals : `int (sin2x)/(cosx)dx`


Evaluate the following integrals:

`int(2)/(sqrt(x) - sqrt(x + 3)).dx`


Integrate the following functions w.r.t. x : sin4x.cos3x


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

`(5 - 3x)(2 - 3x)^(-1/2)`


Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`


Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`


Evaluate the following : `int (1)/(7 + 2x^2).dx`


Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`


Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`


Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`


Evaluate the following : `int (logx)2.dx`


Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx


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


Evaluate the following.

`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx


Evaluate the following.

`int 1/(4x^2 - 20x + 17)` dx


Evaluate the following.

`int 1/(sqrt(3"x"^2 - 5))` dx


Fill in the Blank.

`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


Evaluate: ∫ |x| dx if x < 0


Evaluate: `int "e"^sqrt"x"` dx


`int cos sqrtx` dx = _____________


`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`


`int (f^'(x))/(f(x))dx` = ______ + c.


Evaluated the following

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


Evaluate the following

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


Evaluate:

`int(sqrt(tanx) + sqrt(cotx))dx`


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


`int "cosec"^4x  dx` = ______.


`int 1/(sin^2x cos^2x)dx` = ______.


Evaluate the following.

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


Evaluate the following.

`int1/(x^2 + 4x - 5)  dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×