Question

(a) Find the most general antiderivative of the function f(x) = −x^ −1 + 5√ x / x 2 −=4 csc^2 x

(b) A particle is moving with the given data, where a(t) is acceleration, v(t) is velocity and s(t) is position. Find the position function s(t) of the particle. a(t) = 12t^ 2 − 4, v(0) = 3, s(0) = −1

Answer #1

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) = 4x
+ 7
f(x)=
Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) =
9
x8
f(x)=
f '(t) = sec(t)(sec(t) + tan(t)), −− π/ 2
< t < π/ 2 , f ( π/ 4) = −3
f(t)=
Find f. f '''(x) = cos(x), f(0)...

1) Find the antiderivative if f′(x)=x^6−2x^−2+5 and f(1)=0
2)Find the position function if the velocity is v(t)=4sin(4t)
and s(0)=0

Find the particular antiderivative that satisfies the following
conditions:
A) p'(x)=-20/X^2 ; p(4)=3
B) p'(x)=2x^2-7x ; p(0)=3,000
C) Consider the function f(x)=3cosx−7sinx.
Let F(x) be the antiderivative of f(x) with F(0)=7
D) A particle is moving as given by the data:
v(t)=4sin(t)-7cos(t) ; s(0)=0

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
1.)f(x) = 5/x^4
2.)f(t) = 2+t+t^2 / sqrt (t)
3.)f(x) = 7sqrt(x^2) + xsqrt(x)

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
!.) f(x) =
8x + 3
2.)f(x) =
x2 − 7x + 3
3.)f(x) =
6x5 − 4x4
− 9x2
4.)f(x) =
x(12x + 4)

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is: v(0) = 4 m/
and its initial displacement is s(0) = 5 ms. Find the position of
the particle at t = 1 seconds.
10 m
5 m
11 m
4 m
2m

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) = ⁹√x² +
x√x
F(x) =

Find the most general antiderivative of the function. (Check
your answer by differentiation. Use C for the constant of
the antiderivative.)
f(x) =
11x4/7 +
6x−6/7
f(x)=

A particle is moving with the given data. Find the position
function of the particle a(t)= 10+3t+3t^2, v(0)= 4, s(2) = 10.

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