Advertisements
Advertisements
प्रश्न
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Advertisements
उत्तर
`|"x"| = "x" "when" "x" ≥0`
= `-"x" "when" "x" < 0`
Therefore, `|"x"|/"x"` = 1 when x ≥ 0
= -1 when x < 0
Thus, `int_-1^2 |"x"|/"x"d"x" = int_-1^0 (-1)d"x" + int_0^2 (1)d"x"`
= `-1 xx ["x"]_1^0 + ["x"]_0^2`
= `(-1) [0 + 1] + [2 - 0] = -1 + 2 = 1`.
APPEARS IN
संबंधित प्रश्न
Evaluate: `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate :`int_0^(pi/2)1/(1+cosx)dx`
Evaluate `int_(-1)^2|x^3-x|dx`
Evaluate the integral by using substitution.
`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`
Evaluate the integral by using substitution.
`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)
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:
(i) \[\int x^4 dx\]
Evaluate of the following integral:
Evaluate of the following integral:
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 :
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_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?
If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals ______.
`int_0^(pi4) sec^4x "d"x` = ______.
`int_0^1 sin^-1 ((2x)/(1 + 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
Find: `int (dx)/sqrt(3 - 2x - x^2)`
The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is
