Advertisements
Advertisements
प्रश्न
Find: `int (dx)/sqrt(3 - 2x - x^2)`
Advertisements
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]`
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^(pi/2)1/(1+cosx)dx`
Evaluate: `int1/(xlogxlog(logx))dx`
Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`
Evaluate the integral by using substitution.
`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`
Evaluate the integral by using substitution.
`int_(-1)^1 dx/(x^2 + 2x + 5)`
`int 1/(1 + cos x)` dx = _____
A) `tan(x/2) + c`
B) `2 tan (x/2) + c`
C) -`cot (x/2) + c`
D) -2 `cot (x/2)` + c
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate of the following integral:
(i) \[\int x^4 dx\]
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate:
Evaluate the following integral:
\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .
Evaluate: `int_ e^x ((2+sin2x))/cos^2 x dx`
Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x" d"x"`.
`int_0^3 1/sqrt(3x - x^2)"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
Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.
Evaluate: `int x/(x^2 + 1)"d"x`
