1. Find the area under the curve {image} from x = 1 to x = t
Find the area under the curve {image} from x = 1 to x = t. Evaluate it for t = 10, 100, and 1000 in order to find the total area under the curve for {image} Select the correct answer. The choices give the total area only.
Area = 360
Area = 36
Area = 72 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. The integral is divergent The integral is convergent
Determine whether the following integral is convergent or divergent: {image}
The integral is divergent
The integral is convergent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Area = 66.22 Area = 66.73 Area = 66.24 Area = 66.23
The region { (x, y) | x {image} -7, {image} y {image} } is represented below. Find the area of this region. {applet}
Area = 66.22
Area = 66.73
Area = 66.24
Area = 66.23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. For which of the following functions we can define {image}
f(x)=e-7x2
f(x)=7x
f(x)=-10cos4 x 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Let a and b be real numbers
Let a and b be real numbers. What integral must appear in place of "?" to make the following statement true? {image}
{image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50