Calculus AB
Name__________________________________
Written Assignment 5-2
Calculus AB
Name__________________________________
Written Assignment 5-3
f ( x)  (2 x  3)2 (3x  4)3
Reminder:
Written assignments are supposed to show your best work!
1. Find dy in terms of dx. Simplify.
1. Evaluate
 (4 x  7) dx
3
2. Find dy if x = 1 and dx = -0.1.
2. Harry thinks
3. Find  y if x = 1 and dx = -0.1.
4. Find the error in using dy to approximate  y using these values.
5. Draw a sketch showing dy,  y and this error. (Don’t even try to
make it to scale!)
 x cos xdx  x sin x  cos x  C
prove it. If not, correct it.
. Is he correct? If so,
Calculus AB
Name__________________________________
Written Assignment 5-4
3 10
1 x dx
1. Sketch the graph of the integral. Divide the interval into 4 subintervals of equal sides. Make your graph large enough to be clear!
Calculus AB
Name__________________________________
Written Assignment 5-5
Sketch a graph of an example which shows that the conclusion of
Rolle’s Theorem might not be true if all the hypotheses of the theorem
are not satisfied.
1. All conditions are satisfied except the function is not continuous.
2. Find the upper sum, U 4 . Show work clearly.
2. All conditions are satisfied except the function is not differentiable
at a particular point d in the interval.
3. Find the lower sum, L4 . Show work clearly.
4. Find the midpoint sum, M 4 . Show work clearly.
3. All conditions are satisfied except f ( a )  0.
5. Find the trapezoidal sum, T4 . Show work clearly and don’t use
your program.
6. Complete the inequality showing the relationship among your
answers.
_______  _______  _______  _______
Calculus AB
Name__________________________________
Written Assignment 5-6

5
0
(2 x 2 )dx
1. Evaluate the integral by finding the limit of the sum.
(Use algebra and sigma notation. Be neat and organized.
Use equal signs and make sure you mean it!)
2. Check your answer using Fundamental Theorem of Calculus
Calculus AB
Name__________________________________
Written Assignment 5-7a
Do these without your calculator! Show all steps so I know you
didn’t touch your calculator.
8
1.

2.

3.

1
20x2/3dx
1
1
ln 4
0
4 x  5 dx
e3 x dx
Calculus AB
Name__________________________________
Written Assignment 5-7b

1.5
0
sin x dx
1. Find the value of this integral using the fundamental theorem of
calculus.
Calculus AB
Name__________________________________
Written Assignment 5-8
For each problem, draw a sketch of the region and use the
Fundamental Theorem of Calculus.
1. Find the area bounded by the curves y  0.5 x  2 x and
2
y   x 2  2 x  6 . Find intersection points by completely by hand.
2. By hand, find a midpoint Riemann sum for this integral using 3
sub-intervals of equal length. Show work. Draw a clear sketch
showing the integral and the three rectangles with heights determined
by the midpoints of the sub-intervals.
2. Find the area bounded by the curves y  2e
between x  0 and x  5 .
.2 x
3. Find a midpoint Riemann sum for this integral using 100 subintervals. Write the values you entered into your program.
4. Evaluate this integral using the numerical integration feature on
your calculator. (MATH 9 or CALC 7)
and y  cos x
Calculus AB
Name__________________________________
Written Assignment 5-9
Calculus AB
Name__________________________________
Written Assignment 5-9
Consider the region bounded by the curves x  3  y 4 and x  2 .
Do all these problems using the Fundamental Theorem, showing all
steps WITHOUT your calculator! Leave all answers in exact form.
Consider the region bounded by the curves x  3  y 4 and x  2 .
Do all these problems using the Fundamental Theorem, showing all
steps WITHOUT your calculator! Leave all answers in exact form.
1. Draw a sketch of the region.
1. Draw a sketch of the region.
2. Find the area of the region.
2. Find the area of the region.
(over)
(over)
3. Find the volume of the region if cross sections perpendicular to the
y-axis are equilateral triangles. (Sketch and label the cross section.)
3. Find the volume of the region if cross sections perpendicular to the
y-axis are equilateral triangles. (Sketch and label the cross section.)
4. Find the volume of the solid formed by revolving the region around
the y-axis. (Sketch and label the cross section.)
4. Find the volume of the solid formed by revolving the region around
the y-axis. (Sketch and label the cross section.)