मराठी

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`

उत्तर

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

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

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 7 Integrals
Exercise 7.8 | Q 4 | 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_0^5 (x+1) 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_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_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`


` ∫  log x / x  dx `
 
 
 

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


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

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

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

 


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

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

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

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

 


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

Evaluate the following integral:

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

Evaluate the following integrals as limit of sums:

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

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


Evaluate:

`int (sin"x"+cos"x")/(sqrt(9+16sin2"x")) "dx"`


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 "e"^x "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`


Evaluate the following:

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


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×