मराठी

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`

Advertisements

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Integrals - Exercise 7.8 [पृष्ठ ३३४]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 7 Integrals
Exercise 7.8 | Q 3 | पृष्ठ ३३४

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Evaluate the following definite integrals as limit of sums.

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


Evaluate the following definite integrals as limit of sums.

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


Evaluate the definite integral:

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


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


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`


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`


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

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

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

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

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

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

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

 


Evaluate the following integral:

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

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


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


Evaluate `int_(-1)^2 (7x - 5)"d"x` as a limit of sums


If f and g are continuous functions in [0, 1] satisfying f(x) = f(a – x) and g(x) + g(a – x) = a, then `int_0^"a" "f"(x) * "g"(x)"d"x` is equal to ______.


Evaluate the following as limit of sum:

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


Evaluate the following:

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


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 ______.


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×