Homework 4.4

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Homework 4.4

1. Find the area under the graph of f over the interval

[- 1, 5]

f (x) = \{\begin{cases} x^{2} + 6 & x \leq 3 \\ 5 x & x > 3 \end{cases}

The area is

2. Determine the x-values at which the graphs of f and g cross. If no such x-values exist, state that fact.

$f (x) = x^{2} + 3 x - 2, g (x) = x + 6$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

3. Find the area of the shaded region.

f (x) = 8 x - 2 x^{2} - x^{3}, g (x) = 0

The area is ____

4. Find the area of the shaded region.

$f (x) = x^{4} - 8 x^{3} + 24 x^{2}, g (x) = 19 x + 52$

The area is

5. Find the area of the region bounded by the graphs of the given equations.

y = x, y = x^{5}, x = 0, x = 1

The area is ____

6. Find the area of the region bounded by the graphs of the given equations.

$y = 2 - x^{2}, y = 2 - 4 x$

The area is _____

7. Find the area of the region bounded by the graphs of the given equations.

y = x^{2} + 5, y = x^{2}, x = 0, x = 1

The area is ___

8. Find the average value of the function

f (x) = x^{2} - 15 o n [0, 6]

9. Find the average value over the given interval.

$y = 7 x + 2; [0, b]$

The average value is ____

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This question is taken from Math 2160 – Applied Calculus I » Fall 2021 » Homeworks