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`
Advertisements
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).`
Find :`int(x^2+x+1)/((x^2+1)(x+2))dx`
Find an anti derivative (or integral) of the following function by the method of inspection.
e2x
Find an anti derivative (or integral) of the following function by the method of inspection.
(axe + b)2
Find the following integrals:
`intx^2 (1 - 1/x^2)dx`
Find the following integrals:
`int (ax^2 + bx + c) dx`
Find the following integrals:
`int (x^3 + 5x^2 -4)/x^2 dx`
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
Find the following integrals:
`intsqrtx( 3x^2 + 2x + 3) dx`
Find the following integrals:
`int(2x - 3cos x + e^x) dx`
Find the following integrals:
`int(2x^2 - 3sinx + 5sqrtx) dx`
Find the following integrals:
`int(sec^2x)/(cosec^2x) dx`
Integrate the function:
`1/(sqrt(x+a) + sqrt(x+b))`
Integrate the function:
`1/(x^(1/2) + x^(1/3)) ["Hint:" 1/(x^(1/2) + x^(1/3)) = 1/(x^(1/3)(1+x^(1/6))), "put x" = t^6]`
Integrate the function:
`(e^(5log x) - e^(4log x))/(e^(3log x) - e^(2log x))`
Integrate the function:
`cos x/sqrt(4 - sin^2 x)`
Integrate the function:
`e^x/((1+e^x)(2+e^x))`
Integrate the function:
f' (ax + b) [f (ax + b)]n
Integrate the function:
`(sqrt(x^2 +1) [log(x^2 + 1) - 2log x])/x^4`
Evaluate `int tan^(-1) sqrtx dx`
Find : \[\int\frac{\left( x^2 + 1 \right)\left( x^2 + 4 \right)}{\left( x^2 + 3 \right)\left( x^2 - 5 \right)}dx\] .
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 (sin^2x - cos^2x)/(sin^2x cos^2x) dx` is equal to
`int (xdx)/((x - 1)(x - 2))` equals
`int (dx)/(x(x^2 + 1))` equals
If the normal to the curve y(x) = `int_0^x(2t^2 - 15t + 10)dt` at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value of |a + 6b| is equal to ______.
`int (dx)/sqrt(5x - 6 - x^2)` equals ______.
