# integrals

1. ### help with a definite integral problem

Express the area of the region under the curve y = 6x3 + 7x2 and above the x-axis as a definite integral. answers and explanations please and thank you
2. ### Integrals of Different Metrics (Power & Volumetric Flow Rates)

Hi all, I am trying to understand the implications of taking the integral of different metrics/measurements, specifically energy and volumes. Here's my current understanding as it relates to energy: Energy = power * time. For example, kWh = kW * h. If you take the integral of power over a...
3. ### Evaluating Integrals

I have no clue where to even start: Integral [0,1] (sqrt (4+x^2)sqrt(4-x^2))/(sqrt(16-x^4))
4. ### surface integrals

in the first note , the author stated that the formula of surface area is ſſ sqrt rt ( (∇z/∇x) ^2 + (∇z/∇y)^2 ) +1 ) dA , why in the second notes , it has function of x , y , z in front of sqrt rt ( (∇z/∇x) ^2 + (∇z/∇y)^2 ) +1 ) dA ? Why are the different ? aren't they the same thing ...
5. ### limit of triple integrals

how to get the limit of theta in this question ? in this question , the author found that the linit of theta is from 0 to pi/2 what i did is : since we know that , x= r cos theta , so 1 = 1 cos theta , so , theta = 2pi is the working correct ?
6. ### Indefinite integrals and convergence

Can somebody confirm if this is correct and also i need a little help with the convergence. I think i need to fiind p=Alpha*something. Sorry for bad handwriting Imgur: The most awesome images on the Internet
7. ### Improper Integrals

There are several cases for improper integrals. What is the purpose of this study? I know it involves the limit. Can someone explain this idea in basic terms?
8. ### Volume triple integrals

I need to calculate the volume formed by z=1 and x^2+y^2=8z. Y used cylindrical coordinated and I got r^2=8z and z=1. Is this OK? r from 0 to Sqrt 8 Theta from 0 to 2Pi z from r^2/8 to 1 Thanks
9. ### Fundamental Theorem of Line Integrals

This is another problem from one of my sample tests about line integrals: I know how to get F(x,y), but I have no idea what dr is supposed to be, and how I use y=x^2-1 to determine C.
10. ### Fundamental theorem to find definite integrals

I'm flummoxed by these two problems. The back of the book gives the answers but I'd like to know how to do them. After reviewing my notes, I can't find anything on it. Any help is appreciated 1. Use the fundamental theorem to determine the value of b if the area under the graph of f(x) = x2...
11. ### Trouble with Line Integrals

(Looking at 2.9 and 2.10) Alright so I think if I can actually UNDERSTAND 2.9, 2.10 might be fairly simple. My thoughts so far: Since I'm using a dot product, I'm assuming I'll have to look at F(x) for x1, x2, ... xn. I'm a little uncertain what's being shown other than that, though. Is there...
12. ### Check these two Triple Integrals (cylindrical and spherical)

Sphere Work (the picture I drew is an xy trace of the sphere, if that isn't clear) http://i.imgur.com/WMWUp1D.jpg?1 The sphere problem asks you to find the volume of the region bounded by the plane z=1/2 and a ball with radius 1 centered at the origin using spherical coordinates. I'm not even...
13. ### Calc II Using Integrals to Find Work

I have a problem that I'm not sure how to figure out. It reads, "A tank in the shape of an inverted right circular cone has a height of 9 meters and a radius of 9 meters. It is filled with 5 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the...
14. ### Integrals

Hi everyone, Whilst revising I came across two integrals which I couldn´t solve and I was hoping that someone here could help. They are \int_{-1}^1 \frac{x}{x^6+i} dx and \int_{0}^1 x^m *(log(x))^n dx , m, n \in \mathbb{N}
15. ### Question about Multiple Integrals

I know a lot of you hate it when people post pictures, but for this purpose I need to. I have some questions about integrals. Confusion 1: My book gives steps on how to find limits of multiple integrals, and I am trying to grasp understanding of what they are doing. They say you need to trace...
16. ### Integrals

Hello !I got this assignment last minute while studying for my finals and I would really love some guidance.I don’t know if it is “possible” so if it is not, please tell me.I would like to know if it is possible to “merge” those two equalities so that I get this function : P = f(Tpp). 1) Tpp =...
17. ### Complex Analysis - Integrals

Evaluate $\int_C \frac{coshz}{z-i}dz$ where C is the rectangle with vertices $2, -2, 2 + 4i, -2 + 4i$ oriented counterclockwise
18. ### Estimating Definite integrals

Alright, new day, new question. Thanks for the help before, by the way. There's still some stuff I don't really understand, but I'll have to ask that in its own thread, I think. Just keeping this one for smaller questions. Here is the question I'm working on right now. I've used up 4 of my 5...
19. ### Calculus help needed VLOUME DOUBLE INTEGRALS

Moment Of Inertia help needed!!!!!!!? Find the moments of inertia Ix, Iy, Io of the lamina with the density function p(x,y)=4 and occupying the region D bounded by the lines y-x=5,y+x=-1 and x=3. I am unable to find the intervals for the x range and the y range. QUESTION 2 Use polar...
20. ### Help with Definite Integrals

I have no idea what to do at all with this problem. Could someone give me an answer and explain how it's done? Express the area of the region under the curve y = 6x3 + 7x2 and above the x-axis in the form SAB f(x) dx. (Sorry, I don't know how to type out that one symbol you always see for...