Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
पर्याय
True
False
Advertisements
उत्तर
True
Explanation:
If f(x) = `"e"^("x"^2)`, then
`int "x" * "f"("x") "dx" = int "x" * "e"^("x"^2) *` dx
Put x2 = t
∴ 2x dx = dt
∴ x dx = `1/2` dt
∴ `int "x" * "f"("x") "dx" = 1/2 int "e"^"t" * "dt"`
`= 1/2 "e"^"t" + "c"`
`= 1/2 "e"^("x"^2)` + c
`= 1/2` f(x) + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
The value of \[\int\frac{1}{x + x \log x} dx\] is
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int secx/(secx - tanx)dx` equals ______.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
`int x^3 e^(x^2) dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
