integral

  1. M

    U-subsitution

    Can someone please explain the u-substitution? I don't see a tan(x/2) anywhere in the integral expression.
  2. J

    AP Calc Integrals

    I’m taking AP Calc AB right now, and am practicing for the AP exam. This question allows the use of graphing calculators. Please help me with solving the question below. Thanks in advance!
  3. M

    Minimum volume of empty space in container with water

    Volume of a container is $\frac{4 \pi}{3}$. Water can flow in and out of container.The volume of water in container is given by: $g(t), 0 \leq t \leq 4$, where $t$ is time in hours and $g(t)$ is measured in $m^3$. The rate of change of the volume of water in the container is: $g'(t)= 0.9 - 2.5...
  4. J

    Integral Problem - Power of n

    This is the book answer this is my answer using integration by parts How to convert my answer to the book answer?
  5. J

    Moment of Inertia of a Solid Cone

    How to find the moment of inertia about the z axis of the top half of a solid cone using Spherical Coordinates? This what I did! I = ∫ R^2 dm where I is the moment of inertia and R is the perpendicular distance from the axis of rotation to the slant height of the cone changing dm with...
  6. T

    Triple Integrals; Volume of Solids within Boundaries

    Hello, everyone. So here is the problem in question with their respective answers: Let W1W1 be the solid half-cone bounded by z=x2+y2−−−−−−√z=x2+y2, z=3z=3 and the yzyz-plane with x≥0x≥0, and let Let W2W2 be the solid half-cone bounded by z=x2+y2−−−−−−√z=x2+y2, z=5z=5 and the xzxz-plane with...
  7. S

    How to find integral of following equation?

    I am badly stuck in some integration here and will appreciate any help out of it. $$\int^\infty_0f(r) dr = \int^\infty_0 \frac{Ar}{1+Cr^\alpha} e^{-Br^2} dr$$ If I let $u = Br^2$, then I get $$ = \frac{A}{2B} \int^\infty_0\frac{\exp(-u)}{1+(u/B)^{2/\alpha}} du$$ But I am stuck while...
  8. C

    Help with and improper integral!

    I need help to figure out how can i resolve this improper integral, i don't know what to do with the absolute value: ∞ ∫e^(-lyl) <--- Where lyl is the absolute value of "y", and evaluated from -∞ to ∞ -∞ There is also a photo attached of the integral. Thanks!
  9. E

    Integral of sin x cos2 x sin(cos x) dx

    I need to calculate the integral of sin(x)cos2(x)sin(cos(x)) dx (without specific boundaries) but I'm struggling with this one. Can someone help me?
  10. C

    Integral of (cosx+sinx)^2dx

    I did this but not sure if it is correct: ∫(cosx+sinx)^2dx= ∫(cos^2x+2cosxsinx+sin^2x)= ∫(2cosxsinx)= 2∫cosxsinx= 2sinx-cosx+C <--------End
  11. J

    Riemann Sum for 1/x

    How to find the integral 1/x from 1 to 2 using riemann sum? ∫ 1/x dx = lim as n goes infinity Σ(i = 1 to n)f(xi)Δx Δx = 2-1/n = 1/n xi = 1 + iΔx = 1 + (i/n) = lim as n goes infinity Σ(i = 1 to n)f(1 + (i/n))(1/n) = lim as n goes infinity Σ(i = 1 to n)[ 1 / (1 + (i/n)) ] (1/n) = lim as n goes...
  12. T

    Need help with Volume of 2 Curves about x = 4

    My two equations are y=10ln(x) and y= -x^4 - x + 4. They are bounded below by the x axis. I need to find the volume of the shape obtained by revolving them around the line x=4. I'm not sure what method I should use to solve this, or how I would set it up. Could somebody please help me with this?
  13. V

    volume of this shape

    Hi, I have a little big mathematical problem. I wish to find the volume of this shape below. The volume V seems to be (I'm not sure if the result is correct) this bounded integral. So I need some help to calculate this integral ! Thanks
  14. B

    Line integral of tilted ellipse from lowest point to highest point.

    Compute the line integral of the vector field F<x,y,z> = x2+y2+z2 over the curve of the intersection of z=x+1 and 1=x2+y2. The integration should be from the lowest point to the highest point and counter clockwise when seen from above. So far I paramatized into cylindrical coordinates and got a...
  15. S

    Numerical Analysis

    Hi , Can anyone check for me if I'm doing correctly calculations based on 2 equations? Especially an integral because I don't really know how should I compute it. I'm calculating it in microsoft office excel (I've got those equations from scientific paper, and I don't really know if there is a...
  16. C

    Integral problem with A and c. im very confused, help would be welcomed :)

    This is the question and I'm not entirely sure where to go from here. Thanks! Assume c>0 and A>0, and compute the volume of the solid obtained by revolving the region bound by the graph of f(x)=Ax^2, the vertical line x=c, and the x-axis about the x-axis. Your answer should be in terms of A and...
  17. J

    integral of (1/y)(dy/dx) dx

    Hi there, I'm working through a textbook section on the separation of variables method with respect to differentials and I want to be sure that I understand the why/how/etc. behind the simplification below. Do the dxs just cancel each other out like any simple x, y, etc. variable would? But...
  18. B

    Estimating integral using Taylor Series, extra term

    Hi I have a question to find the Taylor Series for y(x)=ln(1+x) up to and including terms of 0(x^5). I found that series to be: x - 1/2x^(2) + 1/3x^(3) - 1/4x^(4) + 1/5x^(5)...which may or may not be correct! The next part of the question asks: "Use the series to estimate the value of the...
  19. X

    surface integral

    By using the double integral , find surface area of the portion of the surface z = sqrt (4 -x^2) that lies above rectangle in xy -plane whose coordinate dsatisfy 0<x<1 and 0<y<4 ... I have sketched out the diagram , but i found that , it's merely 2 plane surfaces , it's not a 3d object formed...
  20. X

    double integral of surface area

    By using double integral , find the surface area of the portion of plane x +y =z = 3 that lies above disc (x^2) + (y^2) < 2 in first octant… Why shoudnt the surface area be the whole red area + the black area ? Since it’s say lies above disc (x^2) + (y^2) < 2 …Btw, the x^2) + (y^2) < 2 means...