English

Evaluate the Following Definite Integrals as Limit of Sums. `Int_0^4 (X + E^(2x)) Dx` - Mathematics

Advertisements
Advertisements

Question

Evaluate the following definite integrals as limit of sums.

`int_0^4 (x + e^(2x)) dx`

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Integrals - Exercise 7.8 [Page 334]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.8 | Q 6 | Page 334

RELATED QUESTIONS

Evaluate the following definite integrals as limit of sums `int_(-1)^1 e^x dx`


Evaluate the definite integral:

`int_(pi/2)^pi e^x ((1-sinx)/(1-cos x)) dx`


Evaluate the definite integral:

`int_0^(pi/4) (sinx cos x)/(cos^4 x + sin^4 x)`dx


Evaluate the definite integral:

`int_0^(pi/2) (cos^2 x dx)/(cos^2 x + 4 sin^2 x)`


Prove the following:

`int_1^3 dx/(x^2(x +1)) = 2/3 + log  2/3`


Prove the following:

`int_0^1 xe^x dx = 1`


Prove the following:

`int_(-1)^1 x^17 cos^4 xdx = 0`


Prove the following:

`int_0^(pi/2) sin^3 xdx = 2/3`


Evaluate  `int_0^1 e^(2-3x) dx` as a limit of a sum.


`int (cos 2x)/(sin x + cos x)^2dx` is equal to ______.


Choose the correct answers The value of `int_0^1 tan^(-1)  (2x -1)/(1+x - x^2)` dx is 

(A) 1

(B) 0

(C) –1

(D) `pi/4`


Evaluate : `int_1^3 (x^2 + 3x + e^x) dx` as the limit of the sum.


` ∫  log x / x  dx `
 
 
 

\[\int\frac{1}{\sqrt{\tan^{- 1} x} . \left( 1 + x^2 \right)} dx\]

\[\int\frac{\sin x}{\left( 1 + \cos x \right)^2} dx\]

 


\[\int\cot x \cdot \log \text{sin x dx}\]

\[\int x^3 \sin \left( x^4 + 1 \right) dx\]

\[\int4 x^3 \sqrt{5 - x^2} dx\]

\[\int\limits_0^1 \left( x e^x + \cos\frac{\pi x}{4} \right) dx\]

 


Evaluate the following integral:

\[\int\limits_{- 1}^1 \left| 2x + 1 \right| dx\]

\[\int\frac{\sqrt{\tan x}}{\sin x \cos x} dx\]


Evaluate the following as limit of sum:

`int _0^2 (x^2 + 3) "d"x`


Evaluate the following:

`int_0^2 ("d"x)/("e"^x + "e"^-x)`


Evaluate the following:

`int_0^(pi/2) (tan x)/(1 + "m"^2 tan^2x) "d"x`


Evaluate the following:

`int_0^pi x sin x cos^2x "d"x`


Evaluate the following:

`int_0^(1/2) ("d"x)/((1 + x^2)sqrt(1 - x^2))`  (Hint: Let x = sin θ)


The value of `int_(-pi)^pi sin^3x cos^2x  "d"x` is ______.


If f" = C, C ≠ 0, where C is a constant, then the value of `lim_(x -> 0) (f(x) - 2f (2x) + 3f (3x))/x^2` is


Left `f(x) = {{:(1",", "if x is rational number"),(0",", "if x is irrational number"):}`. The value `fof (sqrt(3))` is


The limit of the function defined by `f(x) = {{:(|x|/x",", if x ≠ 0),(0",", "otherwisw"):}`


What is the derivative of `f(x) = |x|` at `x` = 0?


`lim_(n rightarrow ∞)1/2^n [1/sqrt(1 - 1/2^n) + 1/sqrt(1 - 2/2^n) + 1/sqrt(1 - 3/2^n) + ...... + 1/sqrt(1 - (2^n - 1)/2^n)]` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×