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

Integrate the following with respect to the respective variable : 3-2sinxcos2x

Advertisements
Advertisements

प्रश्न

Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`

बेरीज
Advertisements

उत्तर

Let I = `int (3- 2sinx)/(cos^2x)*dx`

= `int(3/(cos^2x) - (2sinx)/(cos^2x))*dx`

= `3 int sec^2x*dx - 2int sec x tanx*dx`

= 3 tan x – 2 sec x + c.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १५०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 2.5 | पृष्ठ १५०

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Integrate : sec3 x w. r. t. x.


Integrate the function in `x^2e^x`.


Integrate the function in x sin−1 x.


Integrate the function in e2x sin x.


Evaluate the following : `int x^2.log x.dx`


Evaluate the following:

`int sec^3x.dx`


Evaluate the following : `int x^3.logx.dx`


Evaluate the following : `int cos sqrt(x).dx`


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

sin (log x)


Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`


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


Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`


Choose the correct options from the given alternatives :

`int tan(sin^-1 x)*dx` =


Choose the correct options from the given alternatives :

`int sin (log x)*dx` =


Integrate the following w.r.t.x : cot–1 (1 – x + x2)


Integrate the following w.r.t.x : log (log x)+(log x)–2 


Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`


Integrate the following w.r.t.x : log (x2 + 1)


Integrate the following w.r.t.x : e2x sin x cos x


Evaluate the following.

`int e^x (1/x - 1/x^2)`dx


Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 


Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx


Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`


`int ("e"^xlog(sin"e"^x))/(tan"e"^x)  "d"x`


Choose the correct alternative:

`intx^(2)3^(x^3) "d"x` =


`int 1/(x^2 - "a"^2)  "d"x` = ______ + c


`int 1/sqrt(x^2 - 8x - 20)  "d"x`


`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?


`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.


`int cot "x".log [log (sin "x")] "dx"` = ____________.


The value of `int "e"^(5x) (1/x - 1/(5x^2))  "d"x` is ______.


Evaluate the following:

`int_0^pi x log sin x "d"x`


The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x))  dx` is


If u and v ore differentiable functions of x. then prove that:

`int uv  dx = u intv  dx - int [(du)/(d) intv  dx]dx`

Hence evaluate `intlog x  dx`


The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.


If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.


Find `int e^x ((1 - sinx)/(1 - cosx))dx`.


Evaluate :

`int(4x - 6)/(x^2 - 3x + 5)^(3/2)  dx`


`intsqrt(1+x)  dx` = ______


Solution of the equation `xdy/dx=y log y` is ______


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


Evaluate:

`int((1 + sinx)/(1 + cosx))e^x dx`


Evaluate the following:

`intx^3e^(x^2)dx` 


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


Evaluate:

`inte^x "cosec"  x(1 - cot x)dx`


Evaluate the following.

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


Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×