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) = 6t² + 4t - 10; s(0) = 0

Particular antiderivatives For the following functions f, find the antiderivative F that satisfies the given condition.

f(x) = (3y + 5)/y; F(1) = 3. y > 0

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

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

d³y/dx³ = 6; y″(0) = −8, y′(0) = 0, y(0) = 5

Solve the initial value problems in Exercises 53–56 for y as a function of x.

(x² + 1)² (dy/dx) = √(x² + 1), where y(0) = 1

Initial Value Problems

Solve the initial value problems in Exercises 71–90.

dy/dx = 1/x² + x, x > 0; y(2) = 1