Chapter 6.1, Problem 3E

To determine

The area using four rectangles of equal width and height.

Answer to Problem 3E

The value of x=25.

Explanation of Solution

Given information:

The x-axis with velocity $$ for time $$

Formula used:

The midpoint rectangular approximation method (MRAM) is used.

Calculation:

  

Since v is function of t area under the curve v (t) gives the particle position. By method of midpoint rectangular approximation method (MRAM), area is divided into rectangles. Total time is divided into four equal intervals and at midpoint of interval calculates the velocity which is equal to height of rectangle then calculates the area of small rectangles then adds all the area.

  

Add all areas to get the position of particle at

  $\begin{array}{l}t=4\\ x=\frac{5}{4}+\frac{13}{4}+\frac{29}{4}+\frac{53}{4}\\ =\frac{100}{4}\\ x=25\end{array}$

Conclusion:

The value of x=25.