1. shadow dancer

    Part of integration

    Hello. I was solving $\int x\arcsin x\, dx$. When applying integration by parts, the book suggests ($v=2x^2-1$), so I came up with this: \frac{1}{4}\left[(2x^2-1)\arcsin x - \!\int \frac {2x^2-1}{\sqrt{1-x^2}}dx\right]. I don't have any idea how the second part is solved. I mean this part: (-...
  2. A

    Converting a limit into an integral.

    When we write $$ \lim_{n\to \infty} \sum_{I=1}^{n} f \left(a+ \frac{(b-a)}{n} i \right) \frac{(b-a)}{n} = \int_{a}^{b} f(x) dx $$ I really get a very big doubt about what is f(x). And most importantly what is $x$? Is $x$ the whole expression $\left(a+ \frac{(b-a)}{n}i\right)$ or $ i \rightarrow...
  3. shadow dancer

    yet another integration problem

    Hi.I've been solving integrals in Piskunov's and I got to this integral . $\int \frac {7x+1}{6x^2+x-1}\,dx$ so I evaluated the integral, but didn't seem to get the answer. The answer the book suggests is $$\frac{2}{3} \ln {(3x-1)} + \frac {1}{2} \ln {(2x+1)} + C$$ but I've come to this thing...
  4. A

    I require a hint in solving this indefinite integral.

    The problem I want to solve is this \int\frac{ (\sin^n \theta - \sin\theta)^{1/n} \cos\theta}{\sin^{n+1}\theta} d\theta Now, if I make a substitution of u = \sin\theta then, the integral would look like this \int \frac{(u^n -u)^{1/n}}{u^{n+1}}du . No matter what substitution I make the...
  5. N


    Integrate the following curve y=f(x) over the stated limit. f(x)=x^3;(2,3)
  6. C

    Idea to solve this integration

    I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...
  7. G

    Is it possible to solve this moment of Inertia by integration?

    Find the moment of Inertia of the cross-sectional area of an I section about its centroidal axis: Is it possible to solve this moment of Inertia by integration?
  8. F


    Hi How we can get integral of f(x)=(9-x^2)^(1/2) without using trigonometric substitution. indefenite integral.
  9. B

    Problem with a simple integration!

    Things I know: \delta ( \tau -1 ) = 1, \tau=1 else \delta ( \tau -1 ) = 0, \tau \neq 1 and \int \delta (\tau -1) = u(\tau -1) where u ( \tau -1 ) = 1, \tau>1 else u ( \tau -1 ) = 0, \tau<1 Integrate to Solve: e^{-2t} \int_{1}^{t}e^{\tau} + e^{2...
  10. A

    Integration over a singularity

    On a recent assignment, my engineering professor gave us a list of functions to treat as integrands and corresponding ranges to integrate them over. We were asked to answer yes or no as to whether they each had a numerical answer. One of the integrands was y = x / (1 - x)^3 with the range x=0 to...
  11. S

    *I need help with this problem*

    Hello everyone, So I started a mathematics research in calculus. I was trying to find which quadratic equation that goes through point A(-5,5) and B(5,5) would give the minimum surface area of revolution. As the general formula of a quadratic function is f(x)=ax^2+bx+c After putting A and...
  12. S


    Integrate the function in the attachment.
  13. S

    Cardioid and integration

    How to find the integral of the function f(x,y) = y over the region D which is inside the cardioid r = 2 + 2 cosθ and outside the circle r=2? I am unable to set the limits of the integrals. Please explain. The answer in my textbook for this comes out to be 22/3. Please show me the answer...
  14. A

    integration of tanh

    How to find definite integral of tanh(A*t-B*t^3) from 0 to 2pi
  15. M

    volume of frustum using integration solid of revolution

    Hi, I am trying to find the volume of the attached solid using integration and solid of revolution. I have worked out the cylinder section but I'm having trouble with the frustum cone section. Q, The metal cover for a piece of machinery is 0.90 m in length, the radius of one end is 20 cm and...
  16. M

    Struggling with 2 integration problems

    So while I'm pretty confident about what the final answers are,but the way I solved the question and the steps they want us to do aren't really matching so I was hoping someone could help me out with these steps?
  17. D

    How to change the order of integration in 3D?

    I have been working on a problem that requires me to integrate in the following way: $$\int_{0}^{\infty} \int_{0}^{y} \int_{0}^{y-x} f(x,y,z)\ dzdxdy$$ I would like to change the order of integration, with dz going last. For the dydxdz option, I've got: $$\int_{0}^{\infty}...
  18. W

    I want a deep understanding of Limits, Differentiation and integration

    Hello :) I'm a teacher in electronics department, I did a light basics of limits, differentiation and integration last semester in just solving problems. But I want a deep understanding of what these topics actually are? Where can I use limits? Is limits still valuable these days? What...
  19. C

    Found this question on a test, tried thrice, no concrete result; help, please.

    Let f(x) be a cubic polynomial with leading coefficient unity such that f(0) = 1 and all the roots of f`(x) = 0 are also roots of f(x) = 0. If integral f(x)dx = g(x) + C, where g(0) = 1/4 and C is constant of integration, then g(3) - g(1) is equal to (A) 27 (B) 48 (C) 60 (D) 81
  20. B

    Is this calculation correct (Double Integration)?

    w = \int_{y_{1}}^{y_{2}} \int_{x_{1}}^{x_{2}} [-m \cdot g + T \cdot \frac{-x + (h - y)}{h}] \cdot dxdy = \int_{y_{1}}^{y_{2}} \int_{x_{1}}^{x_{2}}-m \cdot g \cdot dxdy + \int_{y_{1}}^{y_{2}} \int_{x_{1}}^{x_{2}} T \cdot \frac{-x + (h - y)}{h} \cdot dxdy = -m \cdot g \cdot \int_{y_{1}}^{y_{2}}...