Question

Calculus help?

Answer 1

@dan815 @zepdrix

Answer 2

\[\int\limits -24t^3 -2t = -24 \int\limits t^3 -2 \int\limits t\]

Answer 3

Please paraphrase your question. "wehre does the other integrals fall in" doesn't make a lot of sense.

Answer 4

Try explaining in your own words what you're supposed to do in this problem.

Answer 5

I understand that dumbcow took the constants out. I don't understand what the other part of the question is asking for.... (Is it asking us to plug in those values?)

Answer 6

Yes. First you have to do the anti-differentiation. Your result should consist of two separate definite integrals. These are represented by the several completed integrals. Choose the correct ones to finish finding the numerical value of the original definite integral.
Note that "dt" must be a part of each of these two integrals on the left side.

Answer 7

So for the t^3 plug in 15/4 because on the right side of the question that is what they are telling us t^3 equals?

Answer 8

Yes, that's the basic idea. Pls show all of your work.

Answer 9

ok let me try it.

Answer 10

Some of the info is not needed, e.g. the integral of t^2

Answer 11

Yes, and I was wrong in stating that you need to do actual antidifferentiation.

The 2nd part of the given original definite integral is \[-2\int\limits_{1}^{2}tdt\]

Answer 12

*** 15/4 is what they are telling us t^3 equals?***

I hope you mean that the integral of t^3 from 1 to 2 is 15/4

Answer 13

So this?

Answer 14

Yep @phi

Answer 15

... and the given definite integrals include the integral of tdt from t=1 to t=2.

Answer 16

no, the "whole integral" is 15/4

Answer 17

so it's -24*15/4

Answer 18

ok I'm a little confused. I see that 15/4 and 1 are the whole integrals, but how do we plug that into the other part of the problem since it is an integral?

Answer 19

ok thanks phi il try it

Answer 20

so it's -24*15/4-2*1?

Answer 21

In that case it is -92

Answer 22

So our answer should be -92?

Answer 23

not 1 for the 2nd integral

Answer 24

I'll defer to phi here. Too many cooks will spoil the broth, as the saying goes. I do recommend, CalcHater, that you share all of your work instead of just the final results. That way your helpers can give you more meaningful and relevant feedback.

Answer 25

Oh it should be 3/2 for the second one.

Answer 26

They gave you 4 different integrals, and you use two of them in your problem

Answer 27

they did most work for you , and gave a custom table of the exact integral values you need!

Answer 28

-24*15/4-2*3/2=-93

Answer 29

yes, that looks good

Answer 30

i think this is to check if you know the properties

Answer 31

Alright thanks :) @DanJS I didn't realize they just wanted me to plug in I got confused because I was trying to plug in the t^2 one and I was like this doesnt fit XD

Answer 32

this problem shows
1) the integral of a sum is the sum of the integrals
2) the integral of a scaled function is the scaled integral
i.e. \[ \int a f(x) \ dx = a \int f(x) \ dx\]