Math 1100
Homework 25
15 November, 2013
Name:
1. (5 points) Estimate the area under the graph of y = x2 − 14 x3 between x = 0 and x = 4.
Use four rectangles and evaluate at left endpoints. Draw your rectangles on the picture
below.
2
1
0
1
2
3
4
2. (5 points) Estimate the area under the graph of y = x2 − 14 x3 between x = 0 and x = 4.
Use four rectangles and evaluate at right endpoints. Draw your rectangles on the picture
below.
2
1
0
1
2
3
4
3. (16 points) The following functions all form simple geometric shapes. Sketch each function and use your knowledge of geometry to find the area under each in the range
indicated (not an approximation).
(a) y = 3 from x = 0 to x = t. (Your answer will be a function of t.)
(b) y = 2x from x = 0 to x = t. (Your answer will be a function of t.)
(c) y = x + 1 from x = 0 to x = t. (Your answer will be a function of t.)
(d) What pattern do you notice in your answers above?