Advertisements
Advertisements
Question
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
`int(1-x)^-2.dx`
= `(1-x)^(-2+1)/((-2+1)xx(-1))+"c"`
= `(1-x)^-1/((-1)(-1))+"c"`
= `(1 - x)^-1 + "c"`
APPEARS IN
RELATED QUESTIONS
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`1/(1 + cot x)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
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:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`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)`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int (logx)^2/x dx` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate:
`int sin^2(x/2)dx`
Evaluate `int(1+x+x^2/(2!))dx`
If f'(x) = 4x3 - 3x2 + 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).
