मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Choose the correct options from the given alternatives : If then∫tan3x⋅sec3x⋅dx=(1m)secmx-(1n)secnx+c,then(m,n) = - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct options from the given alternatives :

If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =

पर्याय

  • (5, 3)

  • (3, 5)

  • `(1/5, 1/3)`

  • (4, 4)

MCQ

उत्तर

(5, 3)
[ Hint : `int tan^3x.sec^3x*dx`

= `int sec^2x*tan^2x*secx tanx*dx`

= `int sec^2x(sec^2x - 1)secx tanx*dx`

Put sec x = t].

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 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
पाठ 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.08 | पृष्ठ १४८

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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


Find : `int x^2/(x^4+x^2-2) dx`


Evaluate:

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


Integrate the rational function:

`1/(x^2 - 9)`


Integrate the rational function:

`x/((x-1)(x- 2)(x - 3))`


Integrate the rational function:

`(2x)/(x^2 + 3x + 2)`


Integrate the rational function:

`x/((x^2+1)(x - 1))`


Integrate the rational function:

`x/((x -1)^2 (x+ 2))`


Integrate the rational function:

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


Integrate the rational function:

`(2x)/((x^2 + 1)(x^2 + 3))`


Integrate the rational function:

`1/(x(x^4 - 1))`


Integrate the rational function:

`1/(e^x -1)`[Hint: Put ex = t]


`int (xdx)/((x - 1)(x - 2))` equals:


Find `int (2cos x)/((1-sinx)(1+sin^2 x)) dx`


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


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


Integrate the following w.r.t. x : `(12x + 3)/(6x^2 + 13x - 63)`


Integrate the following w.r.t. x : `(x^2 + x - 1)/(x^2 + x - 6)`


Integrate the following w.r.t. x:

`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`


Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`


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


Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`


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


Integrate the following w.r.t. x : `(1)/(sinx + sin2x)`


Integrate the following with respect to the respective variable : `(6x + 5)^(3/2)`


Integrate the following w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`


Evaluate: `int 1/("x"("x"^5 + 1))` dx


Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx


`int x^7/(1 + x^4)^2  "d"x`


`int x^2sqrt("a"^2 - x^6)  "d"x`


`int sqrt(4^x(4^x + 4))  "d"x`


If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)


`int ((x^2 + 2))/(x^2 + 1) "a"^(x + tan^(-1_x)) "d"x`


`int sqrt((9 + x)/(9 - x))  "d"x`


`int 1/(2 +  cosx - sinx)  "d"x`


`int sec^2x sqrt(tan^2x + tanx - 7)  "d"x`


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


`int (3x + 4)/sqrt(2x^2 + 2x + 1)  "d"x`


`int x^3tan^(-1)x  "d"x`


`int x sin2x cos5x  "d"x`


`int (sin2x)/(3sin^4x - 4sin^2x + 1)  "d"x`


Choose the correct alternative:

`int sqrt(1 + x)  "d"x` =


Choose the correct alternative:

`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =


`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x5 – ______ x3 + 5x + c


State whether the following statement is True or False:

For `int (x - 1)/(x + 1)^3  "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2


Evaluate `int (2"e"^x + 5)/(2"e"^x + 1)  "d"x`


`int 1/(4x^2 - 20x + 17)  "d"x`


Verify the following using the concept of integration as an antiderivative

`int (x^3"d"x)/(x + 1) = x - x^2/2 + x^3/3 - log|x + 1| + "C"`


Evaluate the following:

`int x^2/(1 - x^4) "d"x` put x2 = t


Evaluate the following:

`int (x^2"d"x)/(x^4 - x^2 - 12)`


Evaluate the following:

`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`


Evaluate the following:

`int (2x - 1)/((x - 1)(x + 2)(x - 3)) "d"x`


If `int "dx"/((x + 2)(x^2 + 1)) = "a"log|1 + x^2| + "b" tan^-1x + 1/5 log|x + 2| + "C"`, then ______.


Evaluate: `int (dx)/(2 + cos x - sin x)`


`int 1/(x^2 + 1)^2 dx` = ______.


If `int dx/sqrt(16 - 9x^2)` = A sin–1 (Bx) + C then A + B = ______.


If `int 1/((x^2 + 4)(x^2 + 9))dx = A tan^-1  x/2 + B tan^-1(x/3) + C`, then A – B = ______.


If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.


Evaluate`int(5x^2-6x+3)/(2x-3)dx`


Evaluate.

`int (5x^2 - 6x + 3) / (2x -3) dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×