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Intro to Calculus Final Quiz questions

 
 
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Intro to Calculus Final Quiz questions
by William Meng - Friday, August 16, 2019, 12:40 PM
 

Hello,

I just finished the final quiz, and I had some questions regarding it.

1) For question #17, Why is it 18.29? I thought I messed up my math somewhere, but running the equation through a Riemann Sum calculator got me my answer, which was around 14.29. Is this perhaps just a typo?


2) I'm not sure how to do #20. I've tried to use 1_int_3( 2x^2 - 8) dx, but that got me 1.3333 repeating. 

Some help would be appreciated.


Thanks,

William

 
Picture of David Reynoso
Re: Intro to Calculus Final Quiz questions
by David Reynoso - Monday, August 19, 2019, 2:19 PM
 

Hi William,

For #17 you are correct, the answer (rounded to the nearest hundredth) should be $14.29$. This has been fixed in the quiz so now it should be marked as correct. Thanks for pointing this out!

For #20 we need to split the integral in two portions, since the shaded region is bounded by $f(x)$ and the $x$-axis on the first portion and by $g(x)$ and the $x$-axis on the second portion. The graphs of $f(x) = x^2 + 1$ and $g(x) = -x^2 + 9$ intersect when $x = 2$, so we want to find $$\int_{1}^{2} (x^2 + 1)\, dx + \int_{2}^{3} (-x^2 + 9) \,dx.$$ The first integral is equal to $$\int_{1}^{2} (x^2 + 1) \,dx = \left(\dfrac{x^3}{3} + x\right)\mid_{1}^{2} = \dfrac{10}{3},$$ and the second integral is equal to $$\int_{2}^{3} (-x^2 + 9) \,dx = \left(-\dfrac{x^3}{3} + 9x \right)\mid_{2}^{3} = \dfrac{8}{3},$$ so the area bounded by those graphs and the $x$-axis  is $\dfrac{10}{3} + \dfrac{8}{3} = 6$.

Let us know if you have any other questions!