What is the function y if dy/dx=13x^14+4x^5-2x ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To determine a function, when knowing it's derivative, we'll have to determine te indefinite integral of the expression of derivative.

We'll determine the indefinite integral of f'(x)=13x^14+4x^5-2x.

Int f'(x)dx = f(x) + C

Int (13x^14+4x^5-2x)dx

We'll apply the property of the indefinite integral, to be additive:

Int (13x^14+4x^5-2x)dx = Int (13x^14)dx + Int (4x^5)dx - Int (2x)dx 

Int (13x^14)dx = 13*x^(14+1)/(14+1) + C

Int (13x^14)dx = 13x^15/15 + C (1)

Int (4x^5)dx = 4*x^(5+1)/(5+1) + C

Int (4x^5)dx = 4*x^6/6 + C (2)

Int 2xdx = 2*x^2/2 + C

Int 2xdx = x^2 + C (3)

We'll add: (1)+(2)-(3)

Int (13x^14+4x^5-2x)dx = 13x^15/15 + 4*x^6/6 - x^2 + C

So, the function is:

y = 13x^15/15 + 4*x^6/6 - x^2

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