Question

Determine the antiderivative F of “f” , which is defined by f (x) = 4x3 – 6, where F (0) = 3​
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Answer 1

Given Function :ᶠ (ˣ) = 4ˣ3 – 6

ɴow,integrate the function..

∫4ˣ3 – 6 = 4(ˣ4/4)-6ˣ + ᴄ

∫4ˣ3 – 6 = ˣ4 – 6ˣ + ᴄ

ᴛhus, the antiderivative function is the ,

ғ ⁱˢ ˣ4 – 6ˣ + ᴄ,

where ᴄ is a constant

ᴀlso, given that ,

ғ(0) = 3,

ɴow, substitute ˣ = 0

in the antiderivative function ,

we get (0)4 – 6(0) + ᴄ = 3

ᴛherefore, ᴄ = 3.

ɴow, substitute ᴄ = 3 ⁱⁿ antiderivative function

Hence, the required antiderivative function

isˣ4 – 6ˣ + 3

ʜᵒᵖᵉ ⁱᵗ'ˢ ʰᵉˡᵖ ᵘʰ ❤️

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Answer 2

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