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

Evaluate the following integrals: ∫sin4xcos2x.dx

Advertisements
Advertisements

प्रश्न

Evaluate the following integrals:

`int (sin4x)/(cos2x).dx`

बेरीज
Advertisements

उत्तर

`int (sin4x)/(cos2x).dx`

= `int(2sin 2x cos 2x)/(cos2x).dx`

= `2int sin 2x .dx`

= `2(-(cos2x)/2) + c`

= – cos 2x + 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 3.06 | पृष्ठ १०२

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Integrate the functions:

`sqrt(ax + b)`


Integrate the functions:

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


Integrate the functions:

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


Evaluate: `int (2y^2)/(y^2 + 4)dx`


\[\int\sqrt{3 + 2x - x^2} \text{ dx}\]

\[\int e^x \sqrt{e^{2x} + 1} \text{ dx}\]

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .

Write a value of\[\int \log_e x\ dx\].

 


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


Write a value of

\[\int\frac{a^x}{3 + a^x} \text{ dx}\]

Write a value of\[\int e^{ax} \sin\ bx\ dx\]


Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]


Integrate the following w.r.t. x:

`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`


Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 


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


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


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

`(10x^9 +10^x.log10)/(10^x + x^10)`


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

`(1)/(sinx.cosx + 2cos^2x)`


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


Integrate the following functions w.r.t. x :  tan 3x tan 2x tan x


Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`


Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`


Evaluate the following integral:

`int (3cosx)/(4sin^2x + 4sinx - 1).dx`


Choose the correct option from the given alternatives : 

`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =


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


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


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


Evaluate the following.

`int "x" sqrt(1 + "x"^2)` dx


Evaluate the following.

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


Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx


Choose the correct alternative from the following.

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


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


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


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


State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t


`int sqrt(x^2 + 2x + 5)` dx = ______________


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


`int(log(logx))/x  "d"x`


`int (cos x)/(1 - sin x) "dx" =` ______.


The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.


`int 1/(sinx.cos^2x)dx` = ______.


The value of `sqrt(2) int (sinx  dx)/(sin(x - π/4))` is ______.


`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)


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


Evaluate the following

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


`int "cosec"^4x  dx` = ______.


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


Evaluate the following.

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


For \[t=\cos x\], what is \[dt\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×