मराठी

Evaluate the Following Definite Integrals as Limit of Sums. `Int_(-1)^1 E^X Dx` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following definite integrals as limit of sums `int_(-1)^1 e^x 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 5 | पृष्ठ ३३४

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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_1^4 (x^2 - 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_0^1 dx/(sqrt(1+x) - sqrtx)`


Prove the following:

`int_0^1 xe^x dx = 1`


`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`


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`


` ∫  log x / x  dx `
 
 
 

\[\int\frac{\sin^3 x}{\sqrt{\cos x}} dx\]

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


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

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

 


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

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

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

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

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

 


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


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


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_0^2 ("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^(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 ______.


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


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


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 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×