हिंदी

∫ Sin 3 X Cos X D X

Advertisements
Advertisements

प्रश्न

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

 

योग
Advertisements

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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 18: Indefinite Integrals - Very Short Answers [पृष्ठ १९७]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 18 Indefinite Integrals
Very Short Answers | Q 12 | पृष्ठ १९७

संबंधित प्रश्न

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


Evaluate: `int sqrt(tanx)/(sinxcosx) dx`


Integrate the functions:

`cos x /(sqrt(1+sinx))`


Evaluate : `∫1/(3+2sinx+cosx)dx`


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

Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]


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

 


Write a value of

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

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


Write a value of

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

Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`


Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`


Evaluate the following integrals : `int cos^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 : `(cos3x - cos4x)/(sin3x + sin4x)`


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


Evaluate the following:

`int (1)/(25 - 9x^2)*dx`


Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`


Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`


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


Evaluate the following integrals :  `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`


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


Evaluate the following.

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


`int 1/(cos x - sin x)` dx = _______________


`int (7x + 9)^13  "d"x` ______ + c


Evaluate `int(3x^2 - 5)^2  "d"x`


`int sin^-1 x`dx = ?


`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.


The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.


Write `int cotx  dx`.


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


Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`


Evaluate the following.

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


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


Evaluate `int1/(x(x - 1))dx`


What is integration by substitution?


Which expression results after simplifying \[\int\frac{\sin(t-a)}{\sin t}\,dt\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×