हिंदी

Integrate the function in ex (sinx + cosx). - Mathematics

Advertisements
Advertisements

प्रश्न

Integrate the function in ex (sinx + cosx).

योग

उत्तर

Let `I = int e^x (sin x + cos x)  dx`

Put ex sin x = t

`=> (e^x cos x + e^x sin x) dx = dt`

`therefore e^x (sin x + cos x) dx = dt`

`therefore I = int dt = t + C`

`= e^x sin x + C`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.6 [पृष्ठ ३२८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 7 Integrals
Exercise 7.6 | Q 16 | पृष्ठ ३२८

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Prove that:

`int sqrt(x^2 - a^2)dx = x/2sqrt(x^2 - a^2) - a^2/2log|x + sqrt(x^2 - a^2)| + c`


`int1/xlogxdx=...............`

(A)log(log x)+ c

(B) 1/2 (logx )2+c

(C) 2log x + c

(D) log x + c


Integrate the function in x log 2x.


Integrate the function in x tan-1 x.


Integrate the function in tan-1 x.


Find : 

`∫(log x)^2 dx`


Evaluate the following : `int x^2.log x.dx`


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

sin (log x)


Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`


Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]e 


Choose the correct options from the given alternatives :

`int sin (log x)*dx` =


Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`


Integrate the following with respect to the respective variable : cos 3x cos 2x cos x


Integrate the following w.r.t.x : log (x2 + 1)


Integrate the following w.r.t.x : sec4x cosec2x


Solve the following differential equation.

(x2 − yx2 ) dy + (y2 + xy2) dx = 0


Evaluate the following.

`int "x"^2 "e"^"3x"`dx


Evaluate the following.

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


Evaluate: Find the primitive of `1/(1 + "e"^"x")`


`int (cos2x)/(sin^2x cos^2x)  "d"x`


`int ("d"x)/(x - x^2)` = ______


Choose the correct alternative:

`int ("d"x)/((x - 8)(x + 7))` =


`int "e"^x x/(x + 1)^2  "d"x`


`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.


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


`int_0^1 x tan^-1 x  dx` = ______.


Find: `int e^(x^2) (x^5 + 2x^3)dx`.


Evaluate the following.

`int x^3 e^(x^2) dx`


`int logx  dx = x(1+logx)+c`


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


Evaluate:

`int e^(logcosx)dx`


Evaluate:

`int (sin(x - a))/(sin(x + a))dx`


Evaluate the following:

`intx^3e^(x^2)dx` 


Evaluate the following.

`intx^3e^(x^2) dx`


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


Evaluate:

`int x^2 cos x  dx`


Evaluate the following.

`intx^2e^(4x)dx`


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


Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×