Prepared : Sat Nov 20 11:07:32 CST 1999

MATH 1271

QUIZ VII

1) Evaluate the following indefinite integrals.

First divide the integral into two parts

and work with each separately.

With the first one, use the substitution u=x+1. Then du=dx and the integral becomes

For the second integral, rewrite the quotient as a product and use the power and constant multiple rule.

The final answer will be the sum of the smaller integrals.

Multiply out the term inside the integral.

As we did above integrate each term separately.

Add all the smaller integrals.

2) A particle moves along the x-axis with the acceleration function given by , initial position x(0)=0, and initial velocity v(0)=0. Find the particle's position function x(t).

The position function x is the integral of velocity function v and velocity is the integral of acceleration a. So basically we need to integrate a twice to find x(t).

To find the value of the constant use the initial condition that v(0)=0.

and that equals v(0)=0 by the initial condition. Hence

Now integrate once more to get x(t).

To find the value of the constant use the initial condition on x, x(0)=0.

and that equals x(0)=0 by the initial condition. Hence

This gives us that