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 :

`∫(x+2)/sqrt(x^2+5x+6)dx`


Integrate the functions:

`sqrt(ax + b)`


Integrate the functions:

`((x+1)(x + logx)^2)/x`


Evaluate : `∫1/(3+2sinx+cosx)dx`


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


Write a value of

\[\int e^x \left( \sin x + \cos x \right) \text{ dx}\]

 


Write a value of

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

Write a value of

\[\int\frac{\cos x}{3 + 2 \sin x}\text{  dx}\]

Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].


Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]


Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].


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


Evaluate the following integrals : `int cos^2x.dx`


Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`


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

cos8xcotx


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


Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`


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


Evaluate the following integrals:

`int (7x + 3)/sqrt(3 + 2x - x^2).dx`


Choose the correct options from the given alternatives :

`int sqrt(cotx)/(sinx*cosx)*dx` =


Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =


Evaluate the following.

`int x/(4x^4 - 20x^2 - 3) dx`


Evaluate the following.

`int 1/(sqrt("x"^2 -8"x" - 20))` dx


Evaluate `int "x - 1"/sqrt("x + 4")` dx


`int (cos2x)/(sin^2x)  "d"x`


State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`


State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`


Evaluate `int(3x^2 - 5)^2  "d"x`


`int x^3"e"^(x^2) "d"x`


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


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


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


Evaluate the following.

`int 1/(x^2+4x-5)  dx`


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


Evaluate:

`int sin^3x cos^3x  dx`


Evaluate the following.

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


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


After choosing \[u=g(x)\], what is the next step?


How should a substitution be chosen?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×