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anonymous
 5 years ago
consider the integral
\[\int\limits_{0}^{8} (x+e^x)^2 dx \]
a. use the midpoint rule with n=4 to approximate this integral.
anonymous
 5 years ago
consider the integral \[\int\limits_{0}^{8} (x+e^x)^2 dx \] a. use the midpoint rule with n=4 to approximate this integral.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Expand the square, to get x^2+e^2x+2xe^x and integrate separately

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0not really helping....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i have to use the midpoint rule not just only integrate

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, so with the midpoint rule, you are asked to divide the curve into four rectangles. which means that \[\Delta = (ba)/n \] where b = 8 and a = 0 and n =4 so the width of the sub intervals is \[\Delta=(80)/4 =2 \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\Delta x=\frac {ba}{n}\rightarrow \frac {80}{4}=2\] your intervals are:\[[0,2],[2,4],[4,6],[6,8]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So your subintervals are (0.2), (2,4),(4,6) and (6,8) which means your mid points are at x =1,3,5,7

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so evaluate at the midpoints for each of the subintervals: \[x=1,3,5,7\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks nadeem! big help :D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0therefore according to the rectangle rule, \[\int\limits_{0}^{8}f(x)dx \approx 2 * \sum_{1}^{7}f(x)\] where x takes values 1,3,5,7

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} \ln(x) / x ^{1/2} dx \] to approximate this integral using the trapezoid rule. can you also help me with this :( sorryy

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\Delta x}{2}=\frac{\frac{ba}{n}}{2}\] how many subintervals do you need? you didn't specify Here is the generic equation: \[\int\limits\limits_{0}^{1} \frac{lnx}{\sqrt{x}}dx=\frac {\Delta x}{2}[\frac{lnx_0}{\sqrt{x_0}}+2*\frac {lnx_1}{\sqrt{x_1}}+...+2*\frac{lnx_{n1}}{\sqrt{x_{n1}}}+\frac {lnx_n}{\sqrt{x_n}}]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the question is determine if the improper integral is convergent or divergent. if its convergent, find its value.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here is the problem..... you did posted earlier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah sorry and i got this already thanks, but can you help me with other one i posted on the previous section?
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