Letfbe the function given byf(x)=3xsinx. What is the average value offon the closed interval1x7?

a. -14.764

b. -2.461

c. 1.879

d. 8.161

Question #2 - For timet0, the acceleration of an object moving in a straight line is given bya(t)=ln(3+t⁴). What is the net change in velocity from timet=1to timet=5?

a. -0.204

b. 4.217

c. 5.056

d. 16.868

Question #3 - What is the area of the region in the first quadrant bounded on the left by the graph ofx=y⁴ +y²and on the right by the graph ofx=5y?

a. 2.983

b. 8.508

c. 5005.88

d. 5293.155

Question #4 - If the average value of the functionfon the interval2x6is 3, what is the value of⁶₂ (5f(x)+2)dx?

a. 17

b. 23

c. 62

d. 68

Question #5 - A particle moves along thex-axis with velocity given byv(t)=4t20sin(t²+1)

for timet0. If the particle is at positionx=at timet=0, which of the following gives the position of the particle at timet=4?

A. ⁴₀ (4t20sin(t²+1))dt

B.+⁴0 (4t20sin(t²+1))dt

C. d/dt ((4t20sin(t² +1))_t=4

D. ⁴₀4t20sin(t²+1)dt