English

∫02exdx = ______. - Mathematics and Statistics

Advertisements
Advertisements

Question

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

Options

  • e2 – 1

  • 1 – e2 

  • e – 1

  • 1 – e

MCQ
Fill in the Blanks

Solution

`int_0^2 e^x dx` = `bb(underline(e^2 - 1))`.

Explanation:

`int_0^2 e^xdx = [e^x]_0^2`

= e2 – e0

= e2 – 1

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.6: Definite Integration - Q.1

RELATED QUESTIONS

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_0^1 x(1-x)^n dx`


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

`int_0^(pi/4) log (1+ tan x) dx`


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

`int_((-pi)/2)^(pi/2) sin^2 x  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_0^a  sqrtx/(sqrtx + sqrt(a-x))   dx`


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

`int_0^4 |x - 1| dx`


Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`


Evaluate `int_0^(pi/2) cos^2x/(1+ sinx cosx) dx`


\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.


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 1/("x" [("log x")^2 + 4])  "dx"`


Find `dy/dx, if y = cos^-1 ( sin 5x)`


Evaluate :  ∫ log (1 + x2) dx


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


`int_(-7)^7 x^3/(x^2 + 7)  "d"x` = ______


Evaluate `int_0^1 x(1 - x)^5  "d"x`


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_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?


`int_0^4 1/(1 + sqrtx)`dx = ______.


`int_2^3 x/(x^2 - 1)` dx = ______


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


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


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


f(x) =  `{:{(x^3/k;       0 ≤ x ≤ 2), (0;     "otherwise"):}` is a p.d.f. of X. The value of k is ______


`int_0^{pi/2} cos^2x  dx` = ______ 


If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______


`int_{pi/6}^{pi/3} sin^2x dx` = ______ 


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


If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.


`int_0^{pi/2} (cos2x)/(cosx + sinx)dx` = ______


The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______ 


`int_0^1 "e"^(5logx) "d"x` = ______.


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 ______.


If `int_0^1 "e"^"t"/(1 + "t") "dt"` = a, then `int_0^1 "e"^"t"/(1 + "t")^2 "dt"` is equal to ______.


`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.


If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.


`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"`, then the value of k is:


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


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


If f(x) = `(2 - xcosx)/(2 + xcosx)` and g(x) = logex, (x > 0) then the value of the integral `int_((-π)/4)^(π/4) "g"("f"(x))"d"x` is ______.


Let f be continuous periodic function with period 3, such that `int_0^3f(x)dx` = 1. Then the value of `int_-4^8f(2x)dx` is ______.


Evaluate: `int_1^3 sqrt(x + 5)/(sqrt(x + 5) + sqrt(9 - x))dx`


Evaluate `int_-1^1 |x^4 - x|dx`.


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_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.


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


Evaluate `int_1^2(x+3)/(x(x+2))  dx`


Evaluate the following integral:

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


Solve the following.

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


Evaluate the following integral:

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


Evaluate the following integral:

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


Solve the following.

`int_2^3x/((x+2)(x+3))dx`


Solve the following.

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


Evaluate:

`int_0^6 |x + 3|dx`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×