Just a few checks and a few questions..yes or no will do from most answers thanks =P
1: d/dx of int between x and 1:t^2-2t+3
I got x^2-2x+3..hard huh...
2: find the area between x=3y and x=2+y^2
I got 1/6
3: find the volume of the region bounded by y=4-x^2 and y=0 which is rotated about the x axis:
i got 6pi
4: the base of a solid v is bounded by y=x^2 and y=2-x^2. find the volume if v has square cross sections
I got 32/15 (2.1333333333)
5: a particle has the velocity v(t)=t-1/4*t^2
a) Find: the displacement between 0 and 6 seconds:
b) Explain what this means
c) find the distance travelled between 0 and 6 seconds
d) find the average velocity between 0 and 4 seconds
i got:
a) 0
b) it has arrived back at the starting point
c) 36m
d) help me with this one please
6) use simpsons rule with 4 subsections to approximate the area under sqrt(x-1) between 2 and 5.
I know the answer should be 14/3 however due to the errors in the small amount of subsections could my answer of 6.22 be counted as correct..please try this out yourself with only 4 subsections and see what you get.
7) find the error bound in the result above
i got 1.23596x10^-3, is this correct and can someone please provide the forumla for it too
Sorry question 1 is between 1 and x not between x and 1 so when you subtracted the two substitutions it all become negative.
Question 2: yup ok i will =P(always do just writing quick to save time)
Question 3: I accidentally said rotated about the x axis..its about the y axis lol..is 6pi correct now?
Question 4: would it help if i mentioned that this is like a solid of revolution, but is not formed by revolving the graph(s) so the cross-section is not circle. Integrate the cross-section area with respect to x to get the volume.
Does that help in your answer checking?
Question 5: a) and b) thanks, c) yea i realised that today...first time my working was stupid..., d) thanks for that ill try it.
Captainblack-yes you are correct, thats how i got my answer, i was just trying to explain why mr fantastic got negatives.
Mr fantastic, yes..once again your correct..i did it between 2 and 0 as i imagined the line y=0 as x=0, which cut the rotated region in the wrong place.---so 8pi?
Can you please also recheck the others, im sure im correct for question 4, if anyone knows how to find volumes of non rotated solids by integration feel free to try it out.