हिंदी

Evaluate the Following Definite Integrals as Limit of Sums. `Int_2^3 X^2 Dx` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following definite integrals as limit of sums. 

`int_2^3 x^2 dx`

उत्तर

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Integrals - Exercise 7.8 [पृष्ठ ३३४]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
अध्याय 7 Integrals
Exercise 7.8 | Q 3 | पृष्ठ ३३४

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Evaluate `int_(-1)^2(e^3x+7x-5)dx` as a limit of sums


Evaluate the following definite integrals as limit of sums.

`int_0^5 (x+1) dx`


Evaluate the definite integral:

`int_(pi/2)^pi e^x ((1-sinx)/(1-cos 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_(pi/6)^(pi/3)  (sin x + cosx)/sqrt(sin 2x) dx`


Evaluate the definite integral:

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


Prove the following:

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


Prove the following:

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


Prove the following:

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


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


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


if `int_0^k 1/(2+ 8x^2) dx = pi/16` then the value of k is ________.

(A) `1/2`

(B) `1/3`

(C) `1/4`

(D) `1/5`


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

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


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

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

\[\int\frac{\log x^2}{x} dx\]

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

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

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

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

\[\int\limits_{- \pi/2}^{\pi/2} \sin^4 x\ dx\]

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


Solve: (x2 – yx2) dy + (y2 + xy2) dx = 0 


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_0^1 (x"d"x)/sqrt(1 + x^2)`


Evaluate the following:

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


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


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


Let f: (0,2)→R be defined as f(x) = `log_2(1 + tan((πx)/4))`. Then, `lim_(n→∞) 2/n(f(1/n) + f(2/n) + ... + f(1))` 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×