हिंदी

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)`

योग
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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १५०]

APPEARS IN

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

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If u and v are two functions of x then prove that

`intuvdx=uintvdx-int[du/dxintvdx]dx`

Hence evaluate, `int xe^xdx`


Integrate the function in x sin x.


Integrate the function in (x2 + 1) log x.


`int e^x sec x (1 +   tan x) dx` equals:


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


Evaluate the following : `int x^3.tan^-1x.dx`


Evaluate the following : `int x^2*cos^-1 x*dx`


Evaluate the following : `int sin θ.log (cos θ).dθ`


Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`


Evaluate the following:

`int x.sin 2x. cos 5x.dx`


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

sin (log x)


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


Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`


Choose the correct options from the given alternatives :

`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =


Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`


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


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


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


`int (cos2x)/(sin^2x cos^2x)  "d"x`


Choose the correct alternative:

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


Evaluate `int 1/(x log x)  "d"x`


Evaluate the following:

`int_0^1 x log(1 + 2x)  "d"x`


The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1)  dx` is


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`


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


Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`


If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.


Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.


Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.


Evaluate: 

`int(1+logx)/(x(3+logx)(2+3logx))  dx`


`inte^(xloga).e^x dx` is ______


`int logx  dx = x(1+logx)+c`


`int(f'(x))/sqrt(f(x)) dx = 2sqrt(f(x))+c`


Evaluate `int tan^-1x  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.

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


Evaluate the following.

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


Evaluate the following.

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


Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`


`∫ sin^(−1)` xdx is equal to ______.


Evaluate \[\int \frac{x\sin^{-1}x}{\sqrt{1-x^2}}\,dx.\]


Evaluate \[\int x\cos x\,dx.\]


Evaluate \[\int e^x\sin x\,dx.\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×