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

State whether the following statement is True or False: ∫-55xx2+7 dx = 10 - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

`int_(-5)^5 x/(x^2 + 7)  "d"x` = 10

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

False

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.6: Definite Integration - Q.3

संबंधित प्रश्‍न

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

`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) dx`


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

`int_0^(pi/2)  (cos^5  xdx)/(sin^5 x + cos^5 x)`


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

`int_(-5)^5 | x + 2| dx`


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

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


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

`int_0^pi (x  dx)/(1+ sin x)`


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_0^4 |x - 1| dx`


Evaluate the definite integrals `int_0^pi (x tan x)/(sec x + tan x)dx`


Evaluate: `int_1^4 {|x -1|+|x - 2|+|x - 4|}dx`


`int_0^2 e^x dx` = ______.


`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))  dx` = ______.


Choose the correct alternative:

`int_(-9)^9 x^3/(4 - x^2)  "d"x` =


`int_2^4 x/(x^2 + 1)  "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`


`int_0^{pi/2} xsinx dx` = ______


`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.


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


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


`int_0^1 log(1/x - 1) "dx"` = ______.


`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.


`int_0^1 1/(2x + 5) dx` = ______.


If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0

⇒ `1/4 (square - square)` = 0

⇒ b4 – `square` = 0

⇒ (b2 – a2)(`square` + `square`) = 0

⇒ b2 – `square` = 0 as a2 + b2 ≠ 0

⇒ b = ± `square`


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


Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.


Let `int ((x^6 - 4)dx)/((x^6 + 2)^(1/4).x^4) = (ℓ(x^6 + 2)^m)/x^n + C`, then `n/(ℓm)` is equal to ______.


If f(x) = `{{:(x^2",", "where"  0 ≤ x < 1),(sqrt(x)",", "when"  1 ≤ x < 2):}`, then `int_0^2f(x)dx` equals ______.


The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.


Evaluate: `int_0^π 1/(5 + 4 cos x)dx`


`int_0^(π/4) x. sec^2 x  dx` = ______.


`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.


If `int_0^(2π) cos^2 x  dx = k int_0^(π/2) cos^2 x  dx`, then the value of k is ______.


Evaluate: `int_0^π x/(1 + sinx)dx`.


Solve the following.

`int_1^3 x^2 logx  dx`


If `int_0^1(3x^2 + 2x+a)dx = 0,` then a = ______


Evaluate the following definite integral:

`int_1^3 log x  dx`


Evaluate the following definite integral:

`int_-2^3 1/(x + 5) dx`


Evaluate the following integral:

`int_-9^9x^3/(4-x^2)dx`


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