हिंदी

Choose the correct options from the given alternatives : ∫sinmxcosm+2x⋅dx = - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct options from the given alternatives :

`int (sin^m x)/(cos^(m+2)x)*dx` = 

विकल्प

  • `(tan^(m+1)x)/(m + 1) + c`

  • (m + 2)tanm+1 x + c

  • `tan^mx/m + c`

  • (m + 1)tanm+1 x + c

MCQ

उत्तर

`(tan^(m+1)x)/(m + 1) + c`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Indefinite Integration - Miscellaneous Exercise 3 [पृष्ठ १४८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.04 | पृष्ठ १४८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Prove that:

`int sqrt(a^2 - x^2) dx = x/2 sqrt(a^2 - x^2) + a^2/2sin^-1(x/a)+c`


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`


Evaluate `int_0^(pi)e^2x.sin(pi/4+x)dx`


Integrate the function in x sin x.


Integrate the function in `x^2e^x`.


Integrate the function in xlog x.


Integrate the function in (sin-1x)2.


Integrate the function in (x2 + 1) log x.


Integrate the function in ex (sinx + cosx).


Integrate the function in `((x- 3)e^x)/(x - 1)^3`.


`int e^x sec x (1 +   tan x) dx` equals:


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


Evaluate the following : `int x^3.logx.dx`


Evaluate the following : `int e^(2x).cos 3x.dx`


Evaluate the following : `int log(logx)/x.dx`


Evaluate the following : `int sin θ.log (cos θ).dθ`


Evaluate the following : `int logx/x.dx`


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

`e^-x cos2x`


Integrate the following functions w.r.t. x : `sqrt(5x^2 + 3)`


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


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


If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.


Choose the correct options from the given alternatives :

`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =


Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`


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


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


Integrate the following w.r.t.x : e2x sin x cos x


Evaluate the following.

∫ x log x dx


Evaluate the following.

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


Evaluate the following.

`int "e"^"x" "x - 1"/("x + 1")^3` dx


Evaluate the following.

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


Evaluate the following.

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


Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx


Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx


Evaluate: ∫ (log x)2 dx


`int 1/(4x + 5x^(-11))  "d"x`


Choose the correct alternative:

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


`int 1/x  "d"x` = ______ + c


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


Evaluate `int 1/(x log x)  "d"x`


Evaluate `int (2x + 1)/((x + 1)(x - 2))  "d"x`


`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.


`int cot "x".log [log (sin "x")] "dx"` = ____________.


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


Evaluate the following:

`int_0^1 x log(1 + 2x)  "d"x`


The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1)  dx` is


If u and v ore differentiable functions of x. then prove that:

`int uv  dx = u intv  dx - int [(du)/(d) intv  dx]dx`

Hence evaluate `intlog x  dx`


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


If `int(2e^(5x) + e^(4x) - 4e^(3x) + 4e^(2x) + 2e^x)/((e^(2x) + 4)(e^(2x) - 1)^2)dx = tan^-1(e^x/a) - 1/(b(e^(2x) - 1)) + C`, where C is constant of integration, then value of a + b is equal to ______.


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 ______.


`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.


`int_0^1 x tan^-1 x  dx` = ______.


If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.


Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.


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


`int(1-x)^-2 dx` = ______


`int(3x^2)/sqrt(1+x^3) dx = sqrt(1+x^3)+c`


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


Solve the following

`int_0^1 e^(x^2) x^3 dx`


Evaluate:

`int((1 + sinx)/(1 + cosx))e^x dx`


Evaluate:

`int e^(ax)*cos(bx + c)dx`


Evaluate:

`inte^x sinx  dx`


`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.


Evaluate the following.

`intx^3  e^(x^2) dx`


Complete the following activity:

`int_0^2 dx/(4 + x - x^2) `

= `int_0^2 dx/(-x^2 + square + square)`

= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`

= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`

= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`


Evaluate the following:

`intx^3e^(x^2)dx` 


Evaluate the following.

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


Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×