Find the antiderivative for a function f(x) = 6x3÷4 +6 that satisfies condition F(4) = 63 Evaluate F(x) at point x=2

Question

asked Mar 9, 2021 46.3k views

1 Answer

VCNinc · Answer 1 · 2021-03-15T12:56:10+0000

Answer:

F(2)=-39

Explanation:

We are given:
f(x)=(6)/(4)x^3+6

First, simplify:

f(x)=(3)/(2)x^3+6

Then, find the anti-derivative (integrate). Thus...

$F(x)=\int (f(x)) dx= \int (3)/(2)x^3dx+6 dx$

Simplify:

$(3)/(2) \int x^3dx+6\int 1dx$

Use Power Rule.

Simplify:

(3)/(2) ((1)/(4)x^4)+6x+C

F(x)= (3)/(8)x^4 +6x+C

Now, determine C.

F(4)=63=(3)/(8)(4)^4 +6(4)+C

C=-57

Thus, we have:

F(x)= (3)/(8)x^4 +6x-57

Now, plug in 2.

F(2)=(3)/(8)(2)^4 +6(2)-57

F(2)=-39