हिंदी

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

Advertisements
Advertisements

प्रश्न

Integrate the functions:

sin x ⋅ sin (cos x)

योग

उत्तर

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.2 [पृष्ठ ३०४]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 7 Integrals
Exercise 7.2 | Q 4 | पृष्ठ ३०४

संबंधित प्रश्न

Integrate the functions:

`(sin^(-1) x)/(sqrt(1-x^2))`


Integrate the functions:

`cos x /(sqrt(1+sinx))`


Integrate the functions:

`(1+ log x)^2/x`


Evaluate : `∫1/(3+2sinx+cosx)dx`


Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 


Write a value of

\[\int\frac{1 + \log x}{3 + x \log x} \text{ dx }\] .

Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .


Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]


Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


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

x9.sec2(x10)


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


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

`(10x^9  10^x.log10)/(10^x + x^10)`


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


Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`


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


Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`


Evaluate the following.

`int 1/("x" log "x")`dx


Evaluate the following.

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


Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


Evaluate: `int "e"^sqrt"x"` dx


`int (1 + x)/(x + "e"^(-x))  "d"x`


`int sin^-1 x`dx = ?


If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.


`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?


The value of `intsinx/(sinx - cosx)dx` equals ______.


Evaluated the following

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


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


Evaluate.

`int (5x^2-6x+3)/(2x-3)dx`


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


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


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


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


Evaluate the following:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×