Question

Find the function f(x) satisfying the given conditions. (HINT: You are finding the value of C)

Answer 1

Find \[\int\limits_{}^{}f'(x) dx=f(x)+C, \text{ where } (f)'=f'\]

Answer 2

Or evaluate

Answer 3

Integrate the function given to get from f' to f.

Answer 4

Don't forget when you integrate, put +C.

Answer 5

can u explain? :/

Answer 6

\[\int\limits_{}^{}f'(x) dx=\int\limits_{}^{}(4x^2-1) dx\]
You may find it easy to use the following:
\[\int\limits_{}^{}x^n dx =\frac{x^{n+1}}{n+1}+C, n \neq -1\]
This is because \[(\frac{x^{n+1}}{n+1})'=(n+1) \cdot \frac{x^{n+1-1}}{n+1}=x^{n+1-1}=x^n\]
And you may also want to use
\[\int\limits_{}^{}k dx=kx+C \text{ where} K, C \text{ are a constant} \]

Answer 7

This is because (kx+C)'=(kx)'+(C)'=k(x)'+0+k(x)'=k(1)=k

Answer 8

okay thanks

Answer 9

Are you familiar with the idea of `Integration` yet?
Or has it only been introduced to you as the process of finding the `anti-derivative` so far?

Answer 10

no i'm not familiar

Answer 11

@Best_Mathematician can u help?