Math Insight

Integration problems

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  1. Evaluate the following integral: $\displaystyle \int - \frac{2}{- t + 7}\, dt=$

  2. Find the area bounded by the $x$-axis and the graph of $p{\left (x \right )}=9 e^{4 x}$ between $x=3$ and $x=4$.


    For full credit, do not round your answer to a decimal. (Maximum of 80% credit will be awarded for rounded answers that include at least 5 correct significant digits.)

  3. Evaluate the following integrals.
    1. $\displaystyle \int - 7 t^{5} - 3 t^{3} - 8 t\, dt =$
    2. $\displaystyle\int_{-2}^{0} 10 t^{2} - 9 t + 9\, dt=$

  4. Evaluate the following integrals.
    1. $\displaystyle \int 6 t^{4} - 7 t^{2} - 10 t\, dt =$
    2. $\displaystyle\int 6 e^{- 5 t}\, dt=$
      Need help?

  5. Evaluate the following integral: $\displaystyle\int_{-2}^{0} - t^{2} - 8 t + 4\, dt=$

    If rounding, include at least 5 significant digits in your response.

  6. Approximate the definite integral $\displaystyle \int_{-2}^{-1} - t^{3} + 4\, dt$ using a left Riemann sum with $4$ intervals. If rounding, be sure to include at least $5$ significant digits. (To be safe, include even more digits.)

    $\displaystyle \int_{-2}^{-1} - t^{3} + 4\, dt$
    $\approx$
    $+$
    $+$
    $+$

    $=$

  7. The volume of a cell is given by the function $v{\left (t \right )}=4 t^{2} + 400$ $\mu {\rm m}^3$ from $t=1$ to $t=8$ seconds. What is the average volume of the cell during this time frame?

     $\mu {\rm m}^3$
    For full credit, do not round your answer to a decimal. (Maximum of 80% credit will be awarded for rounded answers that include at least 5 correct significant digits.)

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Math 201, Spring 2017