Reference no: EM131000804

1. Consider the velocity function v(t)= 50e^-2t on the interval 0 ≤ t ≤ 4. Assume t is time measured in seconds and v is velocity measured in meters/second.

(a) Graph the velocity function for 0 ≤ t ≤ 4. Determine when the motion is in the positive direction and when it is in the negative direction.

(b) Determine the displacement over the given interval.

(c) Determine the distance traveled over the given interval.

2. A force of 30 Newton's is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?

3. Consider the region bounded by the graphs y² = 1 - x and y = (x/2) + 1.

(a) Sketch this region carefully.

(b) Calculate the area of the region.

4. Determine the length of the graph of y = ½x² + 3 on the interval [0, 1].

5. Consider the region R bounded by the curve y = √x the x-axis, and the line x = 1. Calculate the volume of the solid of revolution when revolving about the x-axis.

(a) Use x as the variable of integration.

(b) Use y as the variable of integration.

6. Consider the eight integrals below. Do any SEVEN.

(a) ∫1/1+√x dx

(b) ∫(t+4)/(t²+6t+18) dt

(c) ∫x³ ln xdx

(d) ∫√(tanθ) sec⁴ θ dθ

(e) ∫dx/(4+x²)^3/2

(f) ∫(x+3)/(x⁴+9x²) dx

(g) _-t∫^∞ e^-x dx

(h) ₁∫⁵ dx/(x-2)^1/3.