Calculus Midterm

What is the average velocity of y=cosx/x^2+x+2 on the closed interval -1,3?

A. 0.183

A container had the shape obtained by revolving the curve y=sinx+3 from x=0 to x=6 about the x-axis, where x and y are measures in inches. Which is the volume, in cubic inches, of the container?

A. 180.243

The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t)=e^t+te^. What is the average velocity of the particle from time t=0 to t=3?

A. 20.086

Let f be differentiable function such that g(x)exdx=g(x)ex,- 3x2exdx. Which of the following could be g(x)?

A. x^3

The base is a solid is a region in the first quadrant bounded by the x-axis, the y-axis and the line x+2y=8. If cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?

C. 16.755

The length of a curve from x=1 and x=4 is given by the integral of 1 to 4 the square root 1 + 9x4dx. If the curve contains the point (1,6), which of the following could be an equation for this curve?

C. 5+x^3

A particle moves along the x-axis with velocity given by v(t)= 3t^2 +6t for time t>0. If the particle is at position x=2 at time t=0, what is the position of the particle at time t=1?

C. 6

What is the area of the region enclosed by the graphs of y= the square root of 6x-x^2 and y=x/3?

C. 8.541

The region enclosed by the x-axis, the line x=3, and the curve y= the square root of x is rotated about the x-axis. What is the volume of the solid generated

C. 9/2 pi

A particle moves along a straight line, and the graph of the particle's velocity v(t) is shown below for 0<t<5. The particle starts at position s(0)=3. The graph intersects the horizontal axis at t=0,2,&5. Which of the following provides the best interpretation of v(t)dt?

C. The total distance traveled by the particle from t=0 to t=5.

the integral xsin(6x)dx

D. -x/6cos(6x) + 1/36sin(6x) +c

The region bounded by the graph of y=2x-x^2 and the x axis is the base of the solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. What is the volume of the solid?

D. 0.462

The table below gives values of f, f', g and g' for selected values of x. If the integral of 0 to 1 f'(x)g(x)dx =5, then the integral from 0 to 1 f(x)g'(x)dx=

D. 15

Let f be the function defined by f(x)= 2/ the square root of x. What is the average value of f on the interval 4,9?

D. 4/5

When the region enclosed by the graphs of y=x and y= 4x-x^2 is revolved around the x-axis, the volume of the solid is generated is given by

D. pi x the integral of 0 to 3 (x^4-8x^3+15x^2)dx