Advertisements
Advertisements
Question
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)`
Options
True
False
Advertisements
Solution
True
RELATED QUESTIONS
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int x^3"e"^(x^2) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int (1 + x + x^2/(2!)) dx`
