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Integration problems
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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.)
$\displaystyle \int_{-2}^{-1} - t^{3} + 4\, dt$
$\approx$
$+$
$+$
$+$
$=$
Evaluate the following integral: $\displaystyle \int - \frac{2}{- t + 7}\, dt=$
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.)
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.)
Evaluate the following integrals.
$\displaystyle \int - 7 t^{5} - 3 t^{3} - 8 t\, dt =$
$\displaystyle\int_{-2}^{0} 10 t^{2} - 9 t + 9\, dt=$
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.
Evaluate the following integrals.
$\displaystyle \int 6 t^{4} - 7 t^{2} - 10 t\, dt =$
$\displaystyle\int 6 e^{- 5 t}\, dt=$
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e^(x)
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exp(x)
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Math 1241, Fall 2020
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Online exam: Integration exam