हिंदी

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

Advertisements
Advertisements

प्रश्न

Evaluate the following definite integrals as limit of sums.

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

Advertisements

उत्तर

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

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

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 7 Integrals
Exercise 7.8 | Q 4 | पृष्ठ ३३४

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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


Evaluate `int_1^3(e^(2-3x)+x^2+1)dx`  as a limit of sum.


Evaluate the following definite integrals as limit of sums.

`int_a^b x dx`


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_0^4 (x + e^(2x)) dx`


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)`


Evaluate the definite integral:

`int_0^(pi/2) sin 2x tan^(-1) (sinx) dx`


Evaluate the definite integral:

`int_1^4 [|x - 1|+ |x - 2| + |x -3|]dx`


Prove the following:

`int_0^(pi/4) 2 tan^3 xdx = 1 - log 2`


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


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


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

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


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

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

\[\int \sec^4    \text{ x   tan x dx} \]

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

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

 


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

Evaluate the following integrals as limit of sums:

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

Evaluate the following as limit of sum:

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


Evaluate the following:

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


Evaluate the following:

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


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


The value of `lim_(x -> 0) [(d/(dx) int_0^(x^2) sec^2 xdx),(d/(dx) (x sin x))]` is equal to


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


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?


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 ______.


`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 ______.


`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×