Find {eq}f {/eq}.

{eq}\displaystyle f'' (x) = 8 + 6 x + 24 x^2,\ f (0) = 5,\ f (1) = 14 {/eq}.

Question:

Find {eq}f {/eq}.

{eq}\displaystyle f'' (x) = 8 + 6 x + 24 x^2,\ f (0) = 5,\ f (1) = 14 {/eq}.

Important Concept related to Integration:

Suppose we have any function {eq}y=f(x) {/eq}, then the 1st derivative of the function is given by: {eq}f'(x)=\frac{dy}{dx} {/eq}

Hence the primitive of derivative is represented as:

{eq}\int {f'(x)dx} = f(x) + c {/eq}

Answer and Explanation: 1

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Given that;

{eq}f''(x) = 8 + 6x + 24{x^2},f(0) = 5,f(1) = 14; {/eq}

Taking integration in both sides w.r.t 'x';

{eq}\displaystyle f'(x) = 8x +...

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Linear Properties of Definite Integrals

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Chapter 12 / Lesson 8
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The linear properties of definite integrals allow complex problems to be solved. Learn how to differentiate between and to use the zero integral property, backward property, constant property, additive property, and sums property.


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