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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: ∫1+x dx =

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प्रश्न

Choose the correct alternative:

`int sqrt(1 + x)  "d"x` =

पर्याय

  • `x/2 sqrt(1 + x) + "c"`

  • `2/3(1 + x)^(3/2) + "c"`

  • `2/sqrt(1 + x) + "c"`

  • `(-3)/2 (1 + x) + "c"`

MCQ
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उत्तर

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

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पाठ 1.5: Integration - Q.1

संबंधित प्रश्‍न

Integrate the rational function:

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


Integrate the rational function:

`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]


Integrate the rational function:

`1/(e^x -1)`[Hint: Put ex = t]


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


Integrate the following w.r.t. x : `(1)/(2sinx + sin2x)`


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


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


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


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


Evaluate:

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


Evaluate:

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


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


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


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


`int x^7/(1 + x^4)^2  "d"x`


`int 1/(4x^2 - 20x + 17)  "d"x`


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`int (x + sinx)/(1 - cosx)  "d"x`


`int xcos^3x  "d"x`


Evaluate the following:

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


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.


Evaluate: `int_-2^1 sqrt(5 - 4x - x^2)dx`


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


Value of ∫ `(x^2 + 1)/((x − 1)(x − 2))`dx is ______.


Which partial-fraction decomposition is used for \[\frac{\mathrm{p}x+\mathrm{q}}{(x-\mathrm{a})^{2}}\]?


Which partial form is appropriate for \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})^{2}(x-\mathrm{b})}\]?


Which decomposition corresponds to \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})(x^{2}+\mathrm{b}x+\mathrm{c})}\]?


How are the constants \[\mathrm{A},\mathrm{B},\mathrm{C},\ldots\] determined in a partial-fraction decomposition?


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