# integration

1. ### 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: (-...

18. ### 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. ### 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. ### 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}}...