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
Advertisements

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] Standard 12 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` 


Evaluate: `∫8/((x+2)(x^2+4))dx` 


Integrate the rational function:

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


Integrate the rational function:

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


Integrate the rational function:

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


Integrate the rational function:

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


Integrate the rational function:

`1/(e^x -1)`[Hint: Put ex = t]


Evaluate : `∫(x+1)/((x+2)(x+3))dx`


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 : `(2x)/(4 - 3x - x^2)`


Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`


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


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


Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`


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


Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`


Evaluate: `int ("x"^2 + "x" - 1)/("x"^2 + "x" - 6)` dx


Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx


Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx


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


`int (2x - 7)/sqrt(4x- 1) dx`


`int x^7/(1 + x^4)^2  "d"x`


`int 1/(2 +  cosx - sinx)  "d"x`


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


`int x sin2x cos5x  "d"x`


`int (x + sinx)/(1 - cosx)  "d"x`


Evaluate:

`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`


`int 1/(sinx(3 + 2cosx))  "d"x`


`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`


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


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


Evaluate the following:

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


Evaluate the following:

`int "e"^(-3x) cos^3x  "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 ______.


The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.


Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`


Let g : (0, ∞) `rightarrow` R be a differentiable function such that `int((x(cosx - sinx))/(e^x + 1) + (g(x)(e^x + 1 - xe^x))/(e^x + 1)^2)dx = (xg(x))/(e^x + 1) + c`, for all x > 0, where c is an arbitrary constant. Then ______.


Find: `int x^4/((x - 1)(x^2 + 1))dx`.


Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.


Evaluate.

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×