Advertisements
Advertisements
प्रश्न
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
Advertisements
उत्तर
f'(x) = `x - 3/x^3`, f(1) = `11/2` .........[Given]
f(x) = `int"f'"(x) "d"x`
= `int(x - 3/x^3) "d"x`
= `int x "d"x - 3 int x^(-3) "d"x`
= `x^2/2 - 3 (x^(-2)/2) + "c"`
∴f(x) = `x^2/2 + 3/(2x^2) + "c"`
∴ f(1) = `(1)^2/2 + 3/(2(1)^2 + "c"`
∴ `11/2 = 1/2 + 3/2 + "c"`
∴ `11/2` =2 + c
∴ c = `7/2`
Substituting c = `7/2` in (i),, w get
f(x) = `x^2/2 + 3/(2x^2) + 7/2`
संबंधित प्रश्न
Evaluate:
`int x^2/(x^4+x^2-2)dx`
Evaluate: `∫8/((x+2)(x^2+4))dx`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Integrate the rational function:
`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by xn − 1 and put xn = t]
Integrate the rational function:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
Integrate the rational function:
`(2x)/((x^2 + 1)(x^2 + 3))`
Integrate the rational function:
`1/(x(x^4 - 1))`
`int (xdx)/((x - 1)(x - 2))` equals:
`int (dx)/(x(x^2 + 1))` equals:
Integrate the following w.r.t. x : `(x^2 + 2)/((x - 1)(x + 2)(x + 3)`
Integrate the following w.r.t. x:
`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`
Integrate the following w.r.t. x : `((3sin - 2)*cosx)/(5 - 4sin x - cos^2x)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x : `(1)/(2sinx + sin2x)`
Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
Integrate the following w.r.t.x : `sqrt(tanx)/(sinx*cosx)`
Evaluate:
`int (2x + 1)/(x(x - 1)(x - 4)) dx`.
Evaluate:
`int x/((x - 1)^2(x + 2)) dx`
Evaluate: `int 1/("x"("x"^"n" + 1))` dx
`int 1/(x(x^3 - 1)) "d"x`
`int (7 + 4x + 5x^2)/(2x + 3)^(3/2) dx`
`int sqrt((9 + x)/(9 - x)) "d"x`
`int sec^3x "d"x`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int x sin2x cos5x "d"x`
`int xcos^3x "d"x`
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
Evaluate `int (2"e"^x + 5)/(2"e"^x + 1) "d"x`
If `intsqrt((x - 7)/(x - 9)) dx = Asqrt(x^2 - 16x + 63) + log|x - 8 + sqrt(x^2 - 16x + 63)| + c`, then A = ______
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
Evaluate the following:
`int_"0"^pi (x"d"x)/(1 + sin x)`
Evaluate the following:
`int sqrt(tanx) "d"x` (Hint: Put tanx = t2)
Find: `int x^2/((x^2 + 1)(3x^2 + 4))dx`
Let g : (0, ∞) `rightarrow` R be a differentiable function such that `int((x(cosx - sinx))/(e^x + 1) + (g(x)(e^x + 1 - xe^x))/(e^x + 1)^2)dx = (xg(x))/(e^x + 1) + c`, for all x > 0, where c is an arbitrary constant. Then ______.
`int 1/(x^2 + 1)^2 dx` = ______.
If `int dx/sqrt(16 - 9x^2)` = A sin–1 (Bx) + C then A + B = ______.
If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.
Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.
Evaluate`int(5x^2-6x+3)/(2x-3)dx`
Evaluate:
`int x/((x + 2)(x - 1)^2)dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
