हिंदी

Integrate the functions: cosxx

Advertisements
Advertisements

प्रश्न

Integrate the functions:

`cos sqrt(x)/sqrtx`

योग
Advertisements

उत्तर

Let I = `int (cos sqrtx)/sqrtx` dx

Put `sqrt x = t` 

`1/(2 sqrt x)` dx = dt or  `1/sqrt x` dx = 2 dt

Hence, `I = 2 int cos t dt`

`= 2 sin t + C = 2 sin sqrt x + C`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.2 [पृष्ठ ३०५]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.2 | Q 26 | पृष्ठ ३०५

संबंधित प्रश्न

Find: `int(x+3)sqrt(3-4x-x^2dx)`


Find `intsqrtx/sqrt(a^3-x^3)dx`


Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.


 
 

Evaluate :

`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`

 
 

Evaluate: `int sqrt(tanx)/(sinxcosx) dx`


Integrate the functions:

`(log x)^2/x`


`int (dx)/(sin^2 x cos^2 x)` equals:


Write a value of

\[\int\frac{1 + \cot x}{x + \log \sin x} \text{ dx }\]

Write a value of

\[\int e^x \sec x \left( 1 + \tan x \right) \text{ dx }\]

Evaluate the following integrals : `int tanx/(sec x + tan x)dx`


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


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


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


Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.


Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`


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

`(sinx cos^3x)/(1 + cos^2x)`


Evaluate the following:

`int (1)/(25 - 9x^2)*dx`


Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`


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


Evaluate the following.

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


Evaluate the following.

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


Choose the correct alternative from the following.

`int "x"^2 (3)^("x"^3) "dx"` =


If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______


Evaluate `int "x - 1"/sqrt("x + 4")` dx


Evaluate: `int log ("x"^2 + "x")` dx


`int cos^7 x  "d"x`


Evaluate  `int"e"^x (1/x - 1/x^2)  "d"x`


`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?


`int(log(logx) + 1/(logx)^2)dx` = ______.


`int (x + sinx)/(1 + cosx)dx` is equal to ______.


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


Evaluate `int1/(x(x - 1))dx`


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


Evaluate:

`int sqrt((a - x)/x) dx`


The value of `int ("d"x)/(sqrt(1 - x))` is ______.


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


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


After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?


For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×