Advertisements
Advertisements
प्रश्न
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is ______.
विकल्प
`x^4 + 1/x^3 - 129/8`
`x^3 + 1/x^4 + 129/8`
`x^4 + 1/x^3 + 129/8`
`x^3 + 1/x^4 - 129/8`
उत्तर
If `d/dx f(x) = 4x^3 - 3/x^4` such that f(2) = 0, then f(x) is `underline(x^4 + 1/x^3 - 129/8)`.
Explanation:
`d/dx f(x) = 4x^3 - 3/x^4`
= f (x) `= int (4x^3 - 3/x^4) dx`
`= 4/4 x^4 - 3/(-3).1/x^3 + C`
`= x^4 + 1/x^3` + C
But, f(2) = 0
`(2)^4 + 1/(2)^3 + C = 0`
`= 16 + 1/8 + C = 0`
⇒ C `= - 129/8`
⇒ f(x) = `x^4 + 1/x^3 - 129/8`
APPEARS IN
संबंधित प्रश्न
Write the antiderivative of `(3sqrtx+1/sqrtx).`
Evaluate : `∫(sin^6x+cos^6x)/(sin^2x.cos^2x)dx`
If `f(x) =∫_0^xt sin t dt` , then write the value of f ' (x).
Find an anti derivative (or integral) of the following function by the method of inspection.
Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int(sqrtx - 1/sqrtx)^2 dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`intsec x (sec x + tan x) dx`
The anti derivative of `(sqrtx + 1/ sqrtx)` equals:
Integrate the function:
`1/(x^2(x^4 + 1)^(3/4))`
Integrate the function:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
Integrate the function:
`(sin^8 x - cos^8 x)/(1-2sin^2 x cos^2 x)`
Integrate the function:
`1/(cos (x+a) cos(x+b))`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
`cos^3 xe^(log sinx)`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the functions `(sin^(-1) sqrtx - cos^(-1) sqrtx)/ (sin^(-1) sqrtx + cos^(-1) sqrtx) , x in [0,1]`
Integrate the function:
`(2+ sin 2x)/(1+ cos 2x) e^x`
Integrate the function:
`(x^2 + x + 1)/((x + 1)^2 (x + 2))`
Integrate the function:
`tan^(-1) sqrt((1-x)/(1+x))`
Evaluate `int(x^3+5x^2 + 4x + 1)/x^2 dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
Evaluate: `int (1 - cos x)/(cos x(1 + cos x)) dx`
The anti derivative of `(sqrt(x) + 1/sqrt(x))` is equals:
`sqrt((10x^9 + 10^x log e^10)/(x^10 + 10^x)) dx` equals
`int (dx)/(sin^2x cos^2x) dx` equals
`int (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal
`int (xdx)/((x - 1)(x - 2))` equals
What is anti derivative of `e^(2x)`
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
