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Question
Integrate the following with respect to x.
If f'(x) = 8x3 – 2x and f(2) = 8, then find f(x)
Solution
f'(x) = 8x3 – 2x
Integrating both sides of the equation,
`int "f'"(x) "d"x = int 8x^3 "d"x - int 2x "d"x + "c"`
f(x) = `(8x^4)/4 - (2x^2)/2 + "c"`
f(x) = 2x4 – x2 + c
Using f(2) = 8,
8 = 2(2)4 – (2)2 + c
8 = 32 – 4 + c
c = – 20
∴ f(x) = 2x4 – x2 – 20
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