7. Antiderivatives & Indefinite Integrals

Velocity to position Given the following velocity functions of an object moving along a line, find the position function with the given initial position.

v(t) = 2√t; s(0) = 1

Solving initial value problems Find the solution of the following initial value problems.

g'(x) = 7x(x⁶ - 1/7); g(1) = 2

Solving initial value problems Find the solution of the following initial value problems.

y'(Θ) = ((√2 cos³ Θ + 1)/cos² Θ); y (π/4) = 3, -π/2 < Θ < π/2

Velocity to position Given the following velocity functions of an object moving along a line, find the position function with the given initial position.

v(t) = 6t² + 4t - 10; s(0) = 0

Acceleration to position Given the following acceleration functions of an object moving along a line, find the position function with the given initial velocity and position.

a(t) = -32; v(0) = 20, s(0) = 0

Acceleration to position Given the following acceleration functions of an object moving along a line, find the position function with the given initial velocity and position.

a(t) = 2 + 3 sin t; v(0) = 1, s(0) = 10

A car starting at rest accelerates at 16 ft/s² for 5 seconds on a straight road. How far does it travel during this time?

104–107. Functions from derivatives Find the function f with the following properties.

ƒ'(t) = sin t + 2t; ƒ(0) = 5

104–107. Functions from derivatives Find the function f with the following properties.

h'(x) = (x⁴ -2) /(1 + x²) ; h (1) = -(2/3) 

{Use of Tech} Graphing general solutions Graph several functions that satisfy each of the following differential equations. Then find and graph the particular function that satisfies the given initial condition.

f'(x) = 3x + sinx; f(0) = 3