1. What is 3x²cos(x³)dx?   (1 point)

(a) sin 27 – sin 8

(b) 27 sin 27 – 8 sin 8

(c) cos 27 – cos 8

(d) 27 cos 27 – 8 cos 8

2. What is xe^xdx?     (1 point)

(a) 4.5e³

(b) 2e³ + 1

(c) 4e³ – 1

(d) 3e³ – 3

3. What is           (1 point)

(a) ln | x² – 1 | + C

(b) ln | x – 1 | – ln | x + 1 | + C

(c) (ln | x + 1 | – ln | x – 1 |) + C

(d) (ln | x – 1 | – ln | x + 1 |) + C

 4. Which of the following is equal to the area between the curves y = x²– 1 and y = 4x – 4?      (1 point)

(a) [(x² – 1) – (4x – 4)]dx

(b) [ (4x – 4) – ( x² – 1) ]dx

(c) [(x² – 1) – (4x – 4)]dx

(d) [ (4x – 4) – ( x² – 1) ]dx

5. Consider the region defined by y = e ^x, the x-axis, and the lines x = 1 and x = 3. Which of the following is equal to the volume obtained when this region is rotated about the x-axis?     (1 point)

(a) e^x dx

(b) (e^x)² dx

(c) πe^x dx

(d) π(e^x)² dx

6. Suppose that g(x) is increasing and concave down on the interval [a, b] and let I = g(x) dx. If L₁₀₀, R₁₀₀, and T₁₀₀ are respectively the left-hand, right-hand, and trapezoidal sum approximations with 100 equal subdivisions for the integral I, which of the following must be true?      (1 point)

(a) L₁₀₀ < I < T₁₀₀ < R₁₀₀

(b) L₁₀₀< T₁₀₀ < I < R₁₀₀

(c) R₁₀₀< I < T₁₀₀ < L₁₀₀

(d) R₁₀₀ < T₁₀₀ < I < L₁₀₀

(a) the integral converges to 0

(b) the integral converges to 0.5

(c) the integral converges to 1

(d) the integral diverges

(a) 0

(b) 1.5

(c) 2

(d) The series diverges

(a) S₁ converges and S₂ converges

(b) S₁ converges and S₂ diverges

(c) S₁ diverges and S₂ converges

(d) S₁ diverges and S₂ diverges

(a) S₃ converges and S₄ converges

(b) S₃ converges and S₄ diverges

(c) S₃ diverges and S₄ converges

(d) S₃ diverges and S₄ diverges

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

13. What is the interval of convergence of the power series     (1 Point)

(a) – 1 < x < 1

(b) – 1 < x ≤ 1

(c) – 1 ≤ x < 1

(d) – 1 ≤ x ≤ 1

14. What is the solution to the differential equation = 6y that passes through the point (0, 2)?   (1 Point)

(a) y = 2e^6t

(b) y = e^6t + 1

(c) y = 3y² + 2

(d) y = 3t² + 2