1. Calculate the integral (1,0) x^3 dx explicitly by using the Fundamental Theor

Question

1. Calculate the integral (1,0) x^3 dx explicitly by using the Fundamental Theorem of Calculus. Hint: sketch the region.

a. 1/4

b. 5/16

c. 1/2

d. 5/8

e. None of the above

2. Find the area of the region bounded by the curves y = x^2 + 1 and y = 2. Hint: sketch the region.

a. 4/3

b. 2/3

c. 11/9

d. 5/3

e. None of the above

3. Find the area of the region bounded by the curves y = x^2 and y = x. Hint: sketch the region.

a. 1/3

b. 1/9

c. 1/6

d. 5/6

e. None of the above

4. Find the area of the region bounded by the curves y = x^2 and y = x^4. Hint: sketch the region.

a. 4/15

b. 1/6

c. 1/24

d. 1/3

e. None of the above

5. Find the area of the region bounded by the curves y = 2x ? x^2 and y = x^2. Hint: sketch the region.

a. 1/3

b. 1/4

c. 1/5

d. 3/5

e. None of the above

6. Find the area of the region bounded by the curves y = x and y = x^3. Hint: sketch the region.

a. 0

b. 1/4

c. 1/2

d. 1

e. None of the above

7. Find the area of the region bounded by the curves y = x and y = sin(x) and the lines x = 0 and x =

2 . Hint: sketch

the region.

a. 0

b. 1/4

c. 1/2

d. 1

e. None of the above

8. Find the area of the region bounded by the curves y = cos(x) and y = sin(2x) between x = 0 and x=pi/2 . Hint: sketch the region.

a. 1

b. 1/2

c. 1/4

d. 0

e. None of the above

9. Riemann Sums use to approximate the area under a curve.

a. rectangles

b. trapezoids

c. rectangles whose tops are quadratic polynomials (parabolic segments)

d. triangles

e. All of the above

10. Simpson

Explanation / Answer

1.b
2.c
3.a
4.d
5.a
6.c
7.a
8.d
9.b
10.a
11.a
12.c
13.b
14.a
15.a
16.c
17.a

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