Advertisements
Advertisements
Question
Evaluate: ∫ |x| dx if x < 0
Advertisements
Solution
|x| = x; x ≥ 0
= x; x < 0
Let I = ∫ |x| dx, if x < 0
= ∫ - x dx
∴ I = `(- "x"^2)/2` + c
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int(1 - x)^(-2) dx` = ______.
`int (7x + 9)^13 "d"x` ______ + c
`int (cos x)/(1 - sin x) "dx" =` ______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
