मराठी

∫ Sin 3 X Cos X D X - Mathematics

Advertisements
Advertisements

प्रश्न

 Write a valoue of \[\int \sin^3 x \cos x\ dx\]

 

बेरीज

उत्तर

Let I= \[\int\]sin3 x . cos x dx

Let sin x = t
⇒​ cos x dx = dt
\[\therefore I =\]\[\int\] t3 . dt
\[= \frac{t^4}{4} + C\]
\[ = \frac{\sin^4 x}{4} + C \left( \because t = \sin x \right)\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 19: Indefinite Integrals - Very Short Answers [पृष्ठ १९७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 19 Indefinite Integrals
Very Short Answers | Q 12 | पृष्ठ १९७

संबंधित प्रश्‍न

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`


Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`


Integrate the functions:

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


Write a value of

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

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


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


\[\int x \sin^3 x\ dx\]

Find : ` int  (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`


Evaluate the following integrals : tan2x dx


Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`


Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`


Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`


Evaluate the following.

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


Evaluate the following.

`int 1/(x(x^6 + 1))` dx 


Evaluate the following.

`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt


Evaluate the following.

`int 1/(4"x"^2 - 20"x" + 17)` dx


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx


`int (sin4x)/(cos 2x) "d"x`


`int (2 + cot x - "cosec"^2x) "e"^x  "d"x`


`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`


Evaluate `int(3x^2 - 5)^2  "d"x`


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


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


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


`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.


`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.


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


`int dx/(2 + cos x)` = ______.

(where C is a constant of integration)


Evaluated 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:

`int sin^2(x/2)dx`


Evaluate the following.

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


Evaluate `int1/(x(x-1))dx` 


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:

`intsqrt(sec  x/2 - 1)dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×