English

Evaluate the Following Definite Integrals as Limit of Sums. Int_1^4 (X^2 - X) Dx - Mathematics

Advertisements
Advertisements

Question

Evaluate the following definite integrals as limit of sums.

`int_1^4 (x^2 - x) dx`

Advertisements

Solution

From equations (2) and (3), we obtain

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 4 | Page 334

RELATED QUESTIONS

Evaluate the following definite integrals as limit of sums. 

`int_2^3 x^2 dx`


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


Evaluate the definite integral:

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


Evaluate the definite integral:

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


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`


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

\[\int\frac{4x + 3}{\sqrt{2 x^2 + 3x + 1}} dx\]

\[\int e^{cos^2 x}   \text{sin 2x  dx}\]

\[\int\frac{1 + \cos x}{\left( x + \sin x \right)^3} dx\]

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

 


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

\[\text{ ∫  cosec x  log}      \left( \text{cosec x} - \cot x \right) dx\]

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

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

\[\int\frac{1}{x\sqrt{x^4 - 1}} dx\]

\[\int\limits_0^\pi \frac{\sin x}{\sin x + \cos x} dx\]

Evaluate the following integral:

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

Evaluate the following integrals as limit of sums:

\[\int_1^3 \left( 3 x^2 + 1 \right)dx\]

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


Using L’Hospital Rule, evaluate: `lim_(x->0)  (8^x - 4^x)/(4x
)`


Evaluate `int_1^4 ( 1+ x +e^(2x)) dx` as limit of sums.


Evaluate:

`int (sin"x"+cos"x")/(sqrt(9+16sin2"x")) "dx"`


Evaluate the following as limit of sum:

`int_0^2 "e"^x "d"x`


Evaluate the following:

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


Evaluate the following:

`int_(pi/3)^(pi/2) sqrt(1 + cosx)/(1 - cos x)^(5/2)  "d"x`


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


`lim_(x -> 0) (xroot(3)(z^2 - (z - x)^2))/(root(3)(8xz - 4x^2) + root(3)(8xz))^4` is equal to


The value of  `lim_(n→∞)1/n sum_(r = 0)^(2n-1) n^2/(n^2 + 4r^2)` is ______.


`lim_(n→∞){(1 + 1/n^2)^(2/n^2)(1 + 2^2/n^2)^(4/n^2)(1 + 3^2/n^2)^(6/n^2) ...(1 + n^2/n^2)^((2n)/n^2)}` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×