मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Evaluate the following integrals : ∫sin2xcosxdx - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

`int (sin2x)/(cosx)dx = int(2sinx cosx)/cosx dx`

= `2 int sin x dx`
= – 2 cos x + c.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Indefinite Integration - Exercise 3.1 [पृष्ठ १०२]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Indefinite Integration
Exercise 3.1 | Q 2.02 | पृष्ठ १०२

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Integrate the functions:

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


Integrate the functions:

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


Integrate the functions:

`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`


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


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


Write a value of

\[\int e^{2 x^2 + \ln x} \text{ dx}\]

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

 


Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]


\[\text{ If } \int\left( \frac{x - 1}{x^2} \right) e^x dx = f\left( x \right) e^x + C, \text{ then  write  the value of  f}\left( x \right) .\]

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

 

 


Evaluate the following integrals : tan2x dx


Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`


Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`


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

`x^5sqrt(a^2 + x^2)`


Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`


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


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


Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


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


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt"x" + "x")` dx


Fill in the Blank.

`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c


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


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`


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


`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`


`int (logx)^2/x dx` = ______.


Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.


Evaluate 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 the following.

`int 1/(x^2 + 4x - 5)  dx`


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


Solve the following 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 (5x^2 - 6x + 3)/(2x - 3) 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 e^(x^2) dx`


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


Evaluate the following.

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


Evaluate the following

`int x^3 e^(x^2) ` dx


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


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


Evaluate the following.

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


Evaluate the following.

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


Evaluate the following.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×