हिंदी

Write a Value of ∫ E X ( Sin X + Cos X ) D X - Mathematics

Advertisements
Advertisements

प्रश्न

Write a value of

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

 

योग

उत्तर

Let I=\[\int\] ex (sin x + cos xdx

Let ex sin x = t
⇒ (ex . sin x + ex cos xdx = dt

\[\therefore I = \int dt\]
\[ = t + C\]
\[ = e^x \sin x + C \left( \because t = e^x \sin x \right)\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 19: Indefinite Integrals - Very Short Answers [पृष्ठ १९७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Very Short Answers | Q 5 | पृष्ठ १९७

संबंधित प्रश्न

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


Integrate the functions:

`1/(1 + cot x)`


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


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


Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]


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


Evaluate the following integrals : `int(x - 2)/sqrt(x + 5).dx`


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


Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`


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

cos8xcotx


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


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


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


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


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


Choose the correct options from the given alternatives :

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


Choose the correct options from the given alternatives :

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


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


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


Evaluate the following.

`int "x"^3/(16"x"^8 - 25)` dx


Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is


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


State whether the following statement is True or False.

If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`


`int (cos2x)/(sin^2x)  "d"x`


State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`


`int(5x + 2)/(3x - 4) dx` = ______


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


Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.


`int secx/(secx - tanx)dx` equals ______.


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


`int x^2/sqrt(1 - x^6)dx` = ______.


Evaluate the following.

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


Evaluate the following.

`intx sqrt(1 +x^2)  dx`


Evaluate the following.

`intxsqrt(1+x^2)dx`


Evaluate the following:

`int (1) / (x^2 + 4x - 5) dx`


Evaluate `int 1/(x(x-1))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). 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×