Advertisements
Advertisements
प्रश्न
Evaluate: ∫ |x| dx if x < 0
Advertisements
उत्तर
|x| = x; x ≥ 0
= x; x < 0
Let I = ∫ |x| dx, if x < 0
= ∫ - x dx
∴ I = `(- "x"^2)/2` + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: `int 1/(sqrt("x") + "x")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int 1/(xsin^2(logx)) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1)) dx`
