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
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int cos^7 x "d"x`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int (1)/(x(x - 1))dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
