हिंदी

Evaluate the following integrals : ∫1+sin2xdx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`

योग

उत्तर

`int sqrt(1 + sin 2x) dx`

= `intsqrt(cos^2x + sin^2x + 2sin x cos x) dx`

= `intsqrt((cos x + sin x)^2)dx`

= `int(cos x + sinx)dx`

= `int cos x  dx + int sin x  dx`

= sin x – cos x + c.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Exercise 3.1 [पृष्ठ १०२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Indefinite Integration
Exercise 3.1 | Q 2.08 | पृष्ठ १०२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`


Find : `int(x+3)sqrt(3-4x-x^2dx)`


 
 

Evaluate :

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

 
 

Integrate the functions:

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


Integrate the functions:

sin (ax + b) cos (ax + b)


Integrate the functions:

(4x + 2) `sqrt(x^2 + x +1)`


Integrate the functions:

`x^2/(2+ 3x^3)^3`


Integrate the functions:

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


Integrate the functions:

`cos sqrt(x)/sqrtx`


Integrate the functions:

`sqrt(sin 2x) cos 2x`


Integrate the functions:

`(sin x)/(1+ cos x)^2`


Evaluate `int 1/(3+ 2 sinx + cosx) dx`


Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`


\[\int\sqrt{x - x^2} dx\]

Write a value of

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

 


Write a value of

\[\int\frac{\cos x}{3 + 2 \sin x}\text{  dx}\]

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]


Write a value of\[\int\left( e^{x \log_e \text{  a}} + e^{a \log_e x} \right) dx\] .


Write a value of\[\int\frac{\cos x}{\sin x \log \sin x} dx\]

 


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


 Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`


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


Evaluate the following integrals : `int sin x/cos^2x dx`


Evaluate the following integrals:

`int x/(x + 2).dx`


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


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


Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1 


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^n - 1)/sqrt(1 + 4x^n)`


Integrate the following functions w.r.t. x : `cosx/sin(x - a)`


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


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


Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`


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


Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`


Evaluate the following : `int  (1)/(x^2 + 8x + 12).dx`


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


Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`


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


Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`


Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`


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


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


`int logx/(log ex)^2*dx` = ______.


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


If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).


Evaluate the following.

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


Evaluate the following.

`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx


Evaluate the following.

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


Evaluate the following.

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


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


Evaluate `int 1/((2"x" + 3))` dx


`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________


`int (log x)/(log ex)^2` dx = _________


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


`int x/(x + 2)  "d"x`


`int (7x + 9)^13  "d"x` ______ + c


To find the value of `int ((1 + logx))/x` dx the proper substitution is ______


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


`int sin^-1 x`dx = ?


`int(5x + 2)/(3x - 4) dx` = ______


If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.


Find `int dx/sqrt(sin^3x cos(x - α))`.


Evaluate.

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


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


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


Evaluate:

`int sin^3x cos^3x  dx`


Evaluate the following.

`intxsqrt(1+x^2)dx`


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


Evaluate the following:

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


Evaluate the following:

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


Evaluate the following.

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


Evaluate.

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


Evaluate the following.

`int1/(x^2 + 4x-5)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×