मराठी

Write a Value of ∫ E Log S I N X Cos X D X

Advertisements
Advertisements

प्रश्न

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]
बेरीज
Advertisements

उत्तर

Let I= elog sin x . cos x dx 

\[\int\] sin x × cos x dx            \[\left( \because e^{log \text{ a} }= a \right)\]
Let sin x = t
⇒​ cos x dx = dt
\[\therefore I\]\[\int\] t . dt

\[= \frac{t^2}{2} + C\]
\[ = \frac{\sin^2 x}{2} + C \left( \because t = \sin x \right)\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 18: Indefinite Integrals - Very Short Answers [पृष्ठ १९७]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 18 Indefinite Integrals
Very Short Answers | Q 11 | पृष्ठ १९७

संबंधित प्रश्‍न

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`


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


`int (dx)/(sin^2 x cos^2 x)` equals:


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

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

Write a value of

\[\int x^2 \sin x^3 \text{ dx }\]

Write a value of\[\int \cos^4 x \text{ sin x dx }\]


Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]


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


\[If \int e^x \left( \tan x + 1 \right)\text{ sec  x  dx } = e^x f\left( x \right) + C, \text{ then  write  the value  of  f}\left( x \right) .\]

 

 


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


Integrate the following functions w.r.t. x : `(logx)^n/x`


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 : sin4x.cos3x


Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1 


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

`x^5sqrt(a^2 + x^2)`


Evaluate the following:

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


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


Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`


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


Choose the correct options from the given alternatives :

`int f x^x (1 + log x)*dx`


Evaluate the following.

∫ (x + 1)(x + 2)7 (x + 3)dx


Evaluate: `int sqrt(x^2 - 8x + 7)` dx


`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________


If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______


`int (cos2x)/(sin^2x)  "d"x`


If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


If f'(x) = `x + 1/x`, then f(x) is ______.


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


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


Evaluate the following

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


Evaluate:

`int sqrt((a - x)/x) dx`


Evaluate:

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


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


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


Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?


For \[\sqrt{\frac{x-\alpha}{\beta-x}}\] or \[\sqrt{(x-\alpha)(\beta-x)}\], where \[\beta>\alpha\], which substitution is used?


What must be done before integrating after obtaining \[du\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×