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

Choose the correct alternative: ∫-99x34-x2 dx = - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

`int_(-9)^9 x^3/(4 - x^2)  "d"x` =

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पाठ 1.6: Definite Integration - Q.1

संबंधित प्रश्‍न

Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`


Evaluate : `intsec^nxtanxdx`


By using the properties of the definite integral, evaluate the integral:

`int_(pi/2)^(pi/2) sin^7 x dx`


By using the properties of the definite integral, evaluate the integral:

`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`


`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.


\[\int\limits_0^k \frac{1}{2 + 8 x^2} dx = \frac{\pi}{16},\] find the value of k.


Evaluate : `int _0^(pi/2) "sin"^ 2  "x"  "dx"`


The total revenue R = 720 - 3x2 where x is number of items sold. Find x for which total  revenue R is increasing.


Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`


`int_0^1 "e"^(2x) "d"x` = ______


By completing the following activity, Evaluate `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x))  "d"x`.

Solution: Let I = `int_2^5 (sqrt(x))/(sqrt(x) + sqrt(7 - x))  "d"x`     ......(i)

Using the property, `int_"a"^"b" "f"(x) "d"x = int_"a"^"b" "f"("a" + "b" - x)  "d"x`, we get

I = `int_2^5 ("(  )")/(sqrt(7 - x) + "(  )")  "d"x`   ......(ii)

Adding equations (i) and (ii), we get

2I = `int_2^5 (sqrt(x))/(sqrt(x) - sqrt(7 - x))  "d"x + (   )  "d"x`

2I = `int_2^5 (("(    )" + "(     )")/("(    )" + "(     )"))  "d"x`

2I = `square`

∴ I =  `square`


The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x2). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.


`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________


The value of `int_1^3 dx/(x(1 + x^2))` is ______ 


`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?


`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`


`int_-1^1x^2/(1+x^2)  dx=` ______.


`int_0^9 1/(1 + sqrtx)` dx = ______ 


Which of the following is true?


Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`


`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.


`int_(-2)^2 |x cos pix| "d"x` is equal to ______.


`int (dx)/(e^x + e^(-x))` is equal to ______.


`int_(-5)^5  x^7/(x^4 + 10)  dx` = ______.


Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`


Evaluate: `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7) - x)dx`


`int_a^b f(x)dx` = ______.


`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.


`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.


If `lim_("n"→∞)(int_(1/("n"+1))^(1/"n") tan^-1("n"x)"d"x)/(int_(1/("n"+1))^(1/"n") sin^-1("n"x)"d"x) = "p"/"q"`, (where p and q are coprime), then (p + q) is ______.


With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.


`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.


Evaluate `int_0^(π//4) log (1 + tanx)dx`.


Evaluate the following definite integral:

`int_4^9 1/sqrt"x" "dx"`


Evaluate the following integral:

`int_0^1x (1 - x)^5 dx`


Evaluate the following integral:

`int_0^1x(1-x)^5dx`


Evaluate the following definite integral:

`int_-2^3(1)/(x + 5)  dx`


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