Folks, can anyone give me a hand with my calculus homework?

[CarlKillerMiller]

My teacher's been out for a couple of days, so we've had to kinda fend for ourselves. I understand most of the things we've been doing up to now, but I'm having some trouble on calculating integrals by hand. For example:

a=0, t=2, xDx
a=0, t=2 ((x^3)+3x+1)Dx

could anyone please give me a hand with these?

 

[TuxDave]

I have no idea what 'a' and 't' has to do with the problem.

 

[Jon855]

Gives ya my hand...

I'm sure somebody will come along and give you what you need.

 

[CarlKillerMiller]

Originally posted by: TuxDave
I have no idea what 'a' and 't' has to do with the problem.

Well, an integral is the area underneath a line g[x]. a and t are the minimum and maximum values for this line.

 

[KingA21]

Originally posted by: CarlKillerMiller
My teacher's been out for a couple of days, so we've had to kinda fend for ourselves. I understand most of the things we've been doing up to now, but I'm having some trouble on calculating integrals by hand. For example:

a=0, t=2, xDx
a=0, t=2 ((x^3)+3x+1)Dx

could anyone please give me a hand with these?

I don't know what a and t have to do with it (unless those are your limits) but anyways....

xDx = x^2/2

((x^3)+3x+1)Dx = x^4/4 + (3/2)x^2 + x

 

[TuxDave]

Originally posted by: CarlKillerMiller

Originally posted by: TuxDave
I have no idea what 'a' and 't' has to do with the problem.

Well, an integral is the area underneath a line g[x]. a and t are the minimum and maximum values for this line.

So you're saying...

a=0, t=2, xDx

is the same problem as finding the definite integral of "x dx" from x = 0 to 2?

 

[hypn0tik]

In your problems, you need to use the following rules:

Integral (x^n dx) = (1/n+1) x^(n+1) + C, where C is an arbitrary constant, and n is a real number and n is NOT -1.

Also, you need to use the summation property of integrals for your second question. Namely,

Integral ( [f1(x) + f2(x)] dx) = Integral (f1(x)dx) + Integral(f2(x)dx)

Please clarify what a and t are.

 

[CarlKillerMiller]

Originally posted by: TuxDave

Originally posted by: CarlKillerMiller

Originally posted by: TuxDave
I have no idea what 'a' and 't' has to do with the problem.

Well, an integral is the area underneath a line g[x]. a and t are the minimum and maximum values for this line.

So you're saying...

a=0, t=2, xDx

is the same problem as finding the definite integral of "x dx" from x = 0 to 2?

Yes, that's right. So, I'd have to take the antiderivative of each number?

 

[hypn0tik]

Originally posted by: CarlKillerMiller

Originally posted by: TuxDave

Originally posted by: CarlKillerMiller

Originally posted by: TuxDave
I have no idea what 'a' and 't' has to do with the problem.

Well, an integral is the area underneath a line g[x]. a and t are the minimum and maximum values for this line.

So you're saying...

a=0, t=2, xDx

is the same problem as finding the definite integral of "x dx" from x = 0 to 2?

Yes, that's right. So, I'd have to take the antiderivative of each number?

No. You take the anti-derivative of the functions and then substitute in the limits of integration.

For example:

Integral (x dx) from 0 to 1 = 1/2 x^2 (from 0 to 1) = 1/2 (1)^2 - 1/2 (0)^2 = 1/2

Does that help?

 

[Howard]

When evaluating a definite integral (an integral with limits), subtract the integral with the limit on the right-hand-side substituted in by the integral with the limit on the left-hand-side substituted in.

So, S(xdx) = (1/2)x^2 from a to t

Sub t into the integral, then subtract it by the integral when a is subbed in.