Explain how to determine the function when i know the derivativeExample f(x)=? if f'(x)=8x^7-3x^2

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justaguide | College Teacher | (Level 2) Distinguished Educator

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If you know f'(x) and need to find f(x) you have to integrate f'(x).

f(x) = Int [ f'(x) dx]

=> Int [ 8x^7-3x^2 dx]

=> (8/8)*x^8 - (3/3)*x^3 + C

=> x^8 - x^3 + C

The function f(x) = x^8 - x^3 + C

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

According to the rule, f(x) could be determined evaluating the indefinite integral of f'(x)

Int (4x^3+2x)dx

We'll apply the additive property of integrals:

Int (4x^3+2x)dx = Int (4x^3)dx + Int (2x)dx

Int (4x^3+2x)dx = 4 Int x^3 dx + 2 Int x dx

Int (4x^3+2x)dx = 4*x^4/4 + 2*x^2/2

We'll simplify and we'll get:

Int (4x^3+2x)dx = x^4 + x^2 + C

The function f(x) is: f(x) = x^4 + x^2 + C

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