Thread: Integrals

Hello!

I'm having some problems with Calculus. I can't even figure out how to get started, let alone do the problem :S

1)Find derivative of the function:

2)Calculate area enclosed by y^2 = 2x+6 and y = x -1

3) Calculate the integral

Thanks guys

Originally Posted by funnytim

Hello!

I'm having some problems with Calculus. I can't even figure out how to get started, let alone do the problem :S

1)Find derivative of the function:

2)Calculate area enclosed by y^2 = 2x+6 and y = x -1

3) Calculate the integral

Thanks guys

I'll give you a hand with the first one, you try to make some work of your own with the other ones:

Put As the function in the integral is continuous and defined everywhere, the Fundamental Theorem of integral Calculus tells us that

, where is a primitive function of the integrand function, but then:



Tonio

For question three .

Consider

Then make a suitable substitution

1.For your first question see attachment


2. For your second question see second attachment


3.For your third question write sin(2x) = 2sin(x)cos(x)

Then make the substitution u = cos(x) you will obtain -2u/(1+u^2)

in the integrand which you should be able to do

Thanks guys, you're great!

One question in#2 though. After i obtain:




How do I calculate it to obtain the answer, 18?

Thank you again!

Integrate and evaluate at the limits---submit your work if you don't get 18 and I'll see what happened

Actually, while I'm puzzling over that problem, here's another: How do I find a definite integral?

In particular:

Thanks again.

Originally Posted by funnytim

Actually, while I'm puzzling over that problem, here's another: How do I find a definite integral?

In particular:

Thanks again.

Doesn't it look suspiciously similar to a Riemann sum of the function over the interval ?

Tonio