Calculate the following line integral ∫Lydx+xdy for L which is given in the picture below. Line Integral: The line integral of the function with respect to x,y has the following formula ∫f(x,y)dx=∫abf(x(t),y(t))x′(t)dt,∫f(x,y)dy=∫ab...
Some Important Integrals and Formulae: ∫ydxx2+y2=tan−1(xy)∫xdyx2+y2=tan−1(yx)tan−1(x)+tan−1(y)=tan−1(x+y1−xy) Answer and Explanation: The given integral is ∫c(−ydx+xdy)(x2+y2), The given segme...
Answer to: Evaluate the line integral \int_{c}ydx + xdy where C is the parameterized path x = t^2,y= t^3, 2\leq t \leq 6. \int_{c}ydx + xdy =...
Evaluate the line integral ∫Cydx+xdy where C is the parameterized path x=t2,y=t3,1≤t≤6. ∫Cydx+xdy= Evaluating the Line Integral: The line integral formula is ∫C y dx+x dy=∫aby(t)x′ dt+∫abx(t)y′(t) dt. ...
Evaluate the line integral ∫C7ydx+3xdy where C is the straight-line path from (3,2) to (7,4).Line Integral:The line integral is the type of integral which is calculated along with the given path C. The following formula is used to evaluate the lin...