How is $y=\int y' dx$? - Mathematics Stack Exchange
2022年4月6日 · $\begingroup$ I think the intended way to interpret this step is "write the symbol $\int$ on the left of both sides of the equality, and then use $\int \mathrm dy = y$" (possibly …
Evaluate the$\\int_0^1\\int_{\\sin^{-1} y}^{\\pi/2} \\cos x\\sqrt{1 ...
2023年4月11日 · Evaluate the following integrals: \begin{gather} \int_0^1\int_{\sin^{-1} y}^{\pi/2} \cos x\sqrt{1+\cos^2 x}\,dxdy;\\ \int_0^2\int_0^1\int_y^1 \sinh(z^2)\,dzdydx \end ...
Closed form for $\\int_0^1\\int_0^1 \\frac{x y \\sqrt{1-x} \\sqrt{1-y ...
2024年11月15日 · Using only Mathematica and Mellin Transform with Inverse Mellin Transform to solve: $\int _0^1\int _0^1\frac{x y \sqrt{1-x} \sqrt{1-y}}{(x+y)^2}dydx=\\\mathcal{M}_s ...
integration - Evaluate: $ \int_0^1 \int_y^1 e^ {x^2 }dxdy ...
2017年6月7日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
calculus - If $y=\int_0^x f(t)\sin[k(x-t)]dt$, then calculate $\frac{d ...
2015年1月21日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Extremize the functional $J[y]=\\int\\limits_1^2 …
Following the idea Rene gave us, we must add to the Euler-Lagrange equations some restriction. With $$\int\limits_1^2 (y'^{2}+2yy'+y^2)dx=\int\limits_1^2L(x,y,y')dx$$
calculus - Prove that $\int_0^x \int_0^y \int_0^z f (t) dt dz dy ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
integration - $\int\frac{dx}{x-3y}$ when $y(x-y)^2=x
2016年3月30日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Evaluating $\\int y^4(1-y)^3 dy$ using integration by parts
Here is the function which could easily be solved using expansion method but how could I solve it using integration by parts $$\\int y^4(1-y)^3 dy$$ The problem is, when I apply integration by …
calculus - Evaluate $\int_0^1\int_y^\sqrt{y}\frac{y}{\sqrt{x^2+y^2 ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …