#### To determine

**To estimate:**

The work done by the force in moving an object from *x=4* to *x=20* by using themidpoint rule

#### Answer

*112 J*

#### Explanation

**1) Concept:**

Use the midpoint rule to find the work done by considering four subintervals

**2) Calculation:**

With *n=4*, *a=4* and *b=20* the width of a sub-interval is

∆x=b-an

Substitute values,

∆x=20-44

∆x=4

And the midpoints are

x1-=12x0+x1=124+8=1212=6

x2-=12x1+x2=128+12=1220=10

x3-=12x2+x3=1212+16=1228=14

x4-=12x3+x4=1216+20=1236=18

So, the value of integral is

W=∫420f(x)dx≈M4=∑i=14f(xi-)∆x

=∆x(fx1-+fx2-+fx3-+fx4-)

=∆x(f6+f10+f14+f18)

From the given table,

*=4(5.8+8.8+8.2+5.2)*

Simplify,

*=4(28)*

*=112*

Therefore,

*W=112 J*

**Conclusion:**

The work done by the force in moving an object from *x=4* to *x=20* by using the midpoint rule is

*W=112 J*