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

∫01e2xdx = - Mathematics and Statistics

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प्रश्न

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

रिकाम्या जागा भरा

उत्तर

`int_0^1 "e"^(2x) "d"x` =`bbunderline(1/2 ("e"^2 - 1))`

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पाठ 1.6: Definite Integration - Q.2

संबंधित प्रश्‍न

Evaluate : `int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`


Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`


 
 

Evaluate : `intlogx/(1+logx)^2dx`

 
 

Evaluate : `intsec^nxtanxdx`


Evaluate: `int_(-a)^asqrt((a-x)/(a+x)) dx`


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_0^pi (x  dx)/(1+ sin x)`


If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that

\[\int_a^b xf\left( x \right)dx = \left( \frac{a + b}{2} \right) \int_a^b f\left( x \right)dx\]

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


Evaluate : `int 1/("x" [("log x")^2 + 4])  "dx"`


Evaluate :  `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`


Evaluate  : `int "x"^2/("x"^4 + 5"x"^2 + 6) "dx"`


Using properties of definite integrals, evaluate 

`int_0^(π/2)  sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`


`int_2^4 x/(x^2 + 1)  "d"x` = ______


Evaluate `int_1^3 x^2*log x  "d"x`


`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?


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 ______.


The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on ______.


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


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


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


`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______ 


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


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


`int_0^pi x*sin x*cos^4x  "d"x` = ______.


Find `int_0^(pi/4) sqrt(1 + sin 2x) "d"x`


If `f(a + b - x) = f(x)`, then `int_0^b x f(x)  dx` is equal to


Evaluate: `int_((-π)/2)^(π/2) (sin|x| + cos|x|)dx`


`int_0^5 cos(π(x - [x/2]))dx` where [t] denotes greatest integer less than or equal to t, is equal to ______.


If `int_(-a)^a(|x| + |x - 2|)dx` = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then `int_a^(-a)(x + [x])dx` is equal to ______.


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


Evaluate the following integral:

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


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


 `int_-9^9 x^3/(4-x^2) dx` =______


Solve the following.

`int_0^1e^(x^2)x^3 dx`


Evaluate the following integral:

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


Evaluate the following integral:

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


Evaluate the following integral:

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


Evaluate the following integral:

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


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