Find f. (use c for the constant of the first antiderivative, d for the constant of the second antiderivative and e for the constant of the third antiderivative.)
f '''(t) = sqrt(t) − 3 cos(t)
find f. f '''(x) = cos x, f(0) = 7, f '(0) = 6, f ''(0) = 6
a particle is moving with the given data. find the position of the particle.
v(t) = sin(t) − cos(t), s(0) = 3
a particle is moving with the given data. find the position of the particle.
a(t) = t2 − 5t + 3, s(0) = 0, s(1) = 20

(a)

(b)

(c) The position of the particle is

(d) The position of the particle is

Step-by-step explanation:

An anti-derivative of a function f(x) is a function whose derivative is equal to f(x). That is, if F′(x) = f(x), then F(x) is an anti-derivative of f(x).

If F(x) is any anti-derivative of f(x) then the most general anti-derivative of f(x) is called an indefinite integral and denoted,

, c is any constant.

(a) To find f(t) of you must:

1.

2.

3.

(b) To find f(x) of you must:

1.

We use f''(0) = 6 to find the value of C

Thus,

2.

We use f'(0) = 6 to find the value of D

Thus,

3.

We use f(0) = 7 to find the value of E

Thus,

(c) You need to use the relation to find the position of the particle.

We know that , so

We use s(0) = 3 to find the value of C

Therefore, the position of the particle is

(d) You need to use the relation to find the velocity of the particle.

We know that , so

Next, you need to use the relation to find the position of the particle.

We know that , so

We use s(0) = 0, s(1) = 20 to find the value of C and D

Therefore, the position of the particle is

answer:

your answer is: c. 196 7/8 in^3.