Work in a group of at most 4. Explain to those who do not understand. Ask questions if you do not understand.
- A particle moves in a straight line with velocity (in feet per second) given in the graph:
- (15 points) Determine the position function \(s(t)\) at \(t=1\), 2, 3, 4, 5, 6, and 7, assuming \(s(0)=0\).
- (10 points) Sketch a graph of \(s(t)\). Make sure your graph shows
where \(s\) is concave up and where it is concave
down.
- Consider the integral \(\displaystyle \int_{-1}^2(5x-2)\,dx\).
- (15 points) Find a formula to approximate the definite integral using \(n\) subintervals and the Right Hand Rule.
- (10 points) Find the limit of your formula as \(n\rightarrow\infty\) to find the exact value of the definite integral.
- Use the Fundamental Theorem of Calculus to evaluate the integrals:
- (10 points) \(\displaystyle \int_{-1}^2(5x-2)\,dx\)
- (10 points) \(\displaystyle \int_{-2}^{3}(x^2-3)\, dx =\)
- (10 points) \(\displaystyle \int_{\pi/6}^{\pi/4} \csc^2(x)\,dx =\)
- (10 points) \(\displaystyle \int_{1}^{2}\left(\frac{x}{2}-\frac{2}{x}\right) dx =\)
- (10 points) Find \(\displaystyle\frac{d}{dx}\left(\int_{e^x}^{\ln(x)}\sin(t)\,dt\right)\)
Last modified: Tue Apr 5 17:22:12 UTC 2022