Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
विकल्प
True
False
Advertisements
उत्तर
False
Explanation:
Let I = `int "x" * "e"^"2x"` dx
`= "x" int "e"^"2x" * "dx" - int ["d"/"dx" ("x") int "e"^"2x" * "dx"]` dx
`= "x" * "e"^"2x"/2 - int 1 * "e"^"2x"/2 * "dx"`
`= "x"/2 "e"^"2x" - 1/2 int "e"^"2x" +` c
`= "x"/2 "e"^"2x" - 1/2 * "e"^"2x"/2` + c
`= "e"^"2x" ("x"/2 - 1/4)` + c
`= "e"^"2x" (("2x" - 1)/4)` + c
∴ f(x) = `(2"x" - 1)/4`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`sqrt(ax + b)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/("x" log "x")`dx
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
If f'(x) = `x + 1/x`, then f(x) is ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
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)
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
