What is $f (x) = \int - x^{3} + x - 4 d x$ $f(x) = int -x^3+x-4 dx$ if $f (2) = - 3$ $f(2) = -3$ ?

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Answer 1 · 2017-07-25T02:31:52

$f (x) = \int (- x^{3} + x - 4) d x$ $f(x) = int(-x^3+x-4)dx$

Use the power rule to integrate.

$= - \frac{x^{4}}{4} + \frac{x^{2}}{2} - 4 x + C$ $= -x^4/4+x^2/2-4x+C$ $" "$ (item 1)

Find $C$ $C$ by using the fact that $f (2) = - 3$ $f(2) = -3$

$f (x) = - \frac{{(2)}^{4}}{4} + \frac{{(2)}^{2}}{2} - 4 (2) + C = - 3$ $f(x) = -(2)^4/4+(2)^2/2-4(2) + C = -3$

$- 4 + 2 - 8 + C = - 3$ $-4+2-8+C=-3$

$- 10 + C = - 3$ $- 10 +C = -3$

$C = 7$ $C = 7$ $" "$ (item 2)

Combining items (1) and (2), we finish with

$f (x) = - \frac{x^{4}}{4} + \frac{x^{2}}{2} - 4 x + 7$ $f(x) = -x^4/4+x^2/2-4x+7$

What is f(x) = int -x^3+x-4 dxf(x)=∫−x3+x−4dxf(x) = int -x^3+x-4 dx if f(2) = -3 f(2)=−3f(2) = -3 ?