मराठी

Find: ∫dx3-2x-x2 - Mathematics

Advertisements
Advertisements

प्रश्न

Find: `int (dx)/sqrt(3 - 2x - x^2)`

बेरीज

उत्तर

`int (dx)/sqrt(3 - 2x - x^2) = int (dx)/sqrt(-(x^2 + 2x - 3))`

= `int (dx)/sqrt(4 - (x + 1)^2`

= `sin^-1 ((x + 1)/2) + C`  .....`[int (dx)/sqrt(a^2 - x^2) = sin^-1 (x/a) + C]`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2022-2023 (March) Sample

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate: `int1/(xlogxlog(logx))dx`


Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`


If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.


Evaluate: `intsinsqrtx/sqrtxdx`

 


Evaluate the integral by using substitution.

`int_0^2 dx/(x + 4 - x^2)`


Evaluate the integral by using substitution.

`int_(-1)^1 dx/(x^2 + 2x  + 5)`


Evaluate of the following integral: 

\[\int\frac{1}{x^5}dx\]

Evaluate of the following integral: 

\[\int 3^x dx\]

Evaluate : 

\[\int\frac{e^{6 \log_e x} - e^{5 \log_e x}}{e^{4 \log_e x} - e^{3 \log_e x}}dx\]

Evaluate: 

\[\int\frac{1}{a^x b^x}dx\]

Evaluate: 

\[\int\frac{2 \cos^2 x - \cos 2x}{\cos^2 x}dx\]

Evaluate the following definite integral:

\[\int_0^1 \frac{1}{\sqrt{\left( x - 1 \right)\left( 2 - x \right)}}dx\]

Evaluate the following integral:

\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_{- 6}^6 \left| x + 2 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_0^{2\pi} \left| \sin x \right| dx\]

 


Evaluate the following integral:

\[\int\limits_{- \pi/4}^{\pi/4} \left| \sin x \right| dx\]

Evaluate the following integral:

\[\int\limits_2^8 \left| x - 5 \right| dx\]

 


Evaluate each of the following integral:

\[\int_{- \frac{\pi}{4}}^\frac{\pi}{4} \frac{\tan^2 x}{1 + e^x}dx\]

 


Evaluate the following integral:

\[\int_0^{2\pi} \sin^{100} x \cos^{101} xdx\]

 


Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x"  d"x"`.


`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?


`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.


`int_0^1 sin^-1 ((2x)/(1 + x^2))"d"x` = ______.


Evaluate the following:

`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`


Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is


The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is


If `int x^5 cos (x^6)"d"x = "k" sin (x^6) + "C"`, find the value of k.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×