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

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प्रश्न

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

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उत्तर

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पाठ 7: Integrals - Exercise 7.8 [पृष्ठ ३३४]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 7 Integrals
Exercise 7.8 | Q 5 | पृष्ठ ३३४

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संबंधित प्रश्‍न

Evaluate the following definite integrals as limit of sums.

`int_0^5 (x+1) dx`


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


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`int_(pi/2)^pi e^x ((1-sinx)/(1-cos x)) dx`


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_1^3 dx/(x^2(x +1)) = 2/3 + log  2/3`


Prove the following:

`int_0^1 xe^x dx = 1`


Prove the following:

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


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`


` ∫  log x / x  dx `
 
 
 

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

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


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

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

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

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

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

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

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

Evaluate the following integrals as limit of sums:

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

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


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


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


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


What is the derivative of `f(x) = |x|` at `x` = 0?


`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 ______.


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