Question

Calculus 2 - Antiderivatives

Answer 1

\(\large F'(x) = f(x)\)

integrate both sides

\(\large F(x) = \int f(x) dx = \int \frac{1}{4}x dx\)

Answer 2

take the integral ?

Answer 3

x^2/8?

Answer 4

@ganeshie8

Answer 5

\(\large F(x) = \int \frac{1}{4}x dx = \frac{x^2}{8} + c\)

Answer 6

since we're given \(F(0) = 0\), plugin x = 0 in F(x) :-

\(0= 0 + c \implies c = 0 \)

so, the required function will be \(\large F(x) = \frac{x^2}{8}\)

Answer 7

when u take indefinite integral, u wil always get the constant \(c\), dont forget it ok

Answer 8

ok, right

Answer 9

wat do u think about second part ?

Answer 10

somehow get c

Answer 11

??

Answer 12

Is there oly one possible solution ?
the answer is yes. cuz, we oly got one solution when \(c = 0\)