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
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`(1+ log x)^2/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate `int 1/((2"x" + 3))` dx
`int 1/(cos x - sin x)` dx = _______________
`int (cos2x)/(sin^2x) "d"x`
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int(1+x+x^2/(2!))dx`
