मराठी

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

Advertisements
Advertisements

प्रश्न

Integrate the function in ex (sinx + cosx).

बेरीज
Advertisements

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Integrals - Exercise 7.6 [पृष्ठ ३२८]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 7 Integrals
Exercise 7.6 | Q 16 | पृष्ठ ३२८

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Integrate the function in xlog x.


Integrate the function in x (log x)2.


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


Evaluate the following:

`int x.sin 2x. cos 5x.dx`


Integrate the following functions w.r.t. x : `e^(2x).sin3x`


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

`e^-x cos2x`


Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`


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


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

`e^(5x).[(5x.logx + 1)/x]`


Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`


Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)] 


Choose the correct options from the given alternatives :

`int sin (log x)*dx` =


Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`


Evaluate the following.

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


Evaluate the following.

`int "e"^"x" "x"/("x + 1")^2` dx


Evaluate the following.

`int [1/(log "x") - 1/(log "x")^2]` dx


Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 


Choose the correct alternative:

`intx^(2)3^(x^3) "d"x` =


`int (x^2 + x - 6)/((x - 2)(x - 1))  "d"x` = x + ______ + c


`int log x * [log ("e"x)]^-2` dx = ?


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


Evaluate the following:

`int_0^pi x log sin x "d"x`


`int tan^-1 sqrt(x)  "d"x` is equal to ______.


The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x))  dx` is


State whether the following statement is true or false.

If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.


If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.


The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.


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


Solution of the equation `xdy/dx=y log y` is ______


Evaluate the following.

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


Evaluate `int(3x-2)/((x+1)^2(x+3))  dx`


`int logx  dx = x(1+logx)+c`


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


Evaluate:

`int1/(x^2 + 25)dx`


If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×