मराठी

Evaluate the Following Definite Integrals as Limit of Sums. Int_A^B X Dx - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following definite integrals as limit of sums.

`int_a^b x dx`

उत्तर

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 1 | पृष्ठ ३३४

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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_2^3 x^2 dx`


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


Evaluate the following definite integrals as limit of sums.

`int_0^4 (x + e^(2x)) 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_(pi/6)^(pi/3)  (sin x + cosx)/sqrt(sin 2x) dx`


Evaluate the definite integral:

`int_0^(pi/4) (sin x +  cos x)/(9+16sin 2x) dx`


Evaluate the definite integral:

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


Prove the following:

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


Prove the following:

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


Prove the following:

`int_0^1sin^(-1) xdx = pi/2 - 1`


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


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

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

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

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

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

\[\int\limits_{- \pi/2}^{\pi/2} \sin^4 x\ dx\]

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


Using L’Hospital Rule, evaluate: `lim_(x->0)  (8^x - 4^x)/(4x
)`


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


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


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


`lim_(x -> 0) (xroot(3)(z^2 - (z - x)^2))/(root(3)(8xz - 4x^2) + root(3)(8xz))^4` is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×