NettetFree math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. NettetSplit the single integral into multiple integrals. Apply the constant rule. Since −1 - 1 is constant with respect to y y, move −1 - 1 out of the integral. Let u = 2y u = 2 y. Then du = 2dy d u = 2 d y, so 1 2du = dy 1 2 d u = d y. Rewrite using u u and d d u u. Tap for more steps... Combine cos(u) cos ( u) and 1 2 1 2.
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NettetGiven, (y²−1)dx = 2dy ==> dx/dy = 2/ (y²−1) ==> ∫dx = 2∫dy/ (y²−1) ==> x + c = ∫ [ (1/ (y-1) - (1/ (y+1)]dy = ln (y-1)-ln (y+1) = ln { (y-1)/ (y+1)} or (y - 1)/ (y + 1) = e^ (x+c), where c is arbitrary constant etc. 5 More answers below Quora User Student (1988–present) Author has 886 answers and 1.1M answer views 7 y Related NettetCalculus Evaluate the Integral integral of x/ (x^2+y^2) with respect to y ∫ x x2 + y2 dy ∫ x x 2 + y 2 d y Since x x is constant with respect to y y, move x x out of the integral. x∫ 1 … christian laughlin
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NettetHow do you integrate Y (x + y) dx + (x + 2y − 1) dy = 0? The equation is in the form M (x,y)dx+ N (x,y)dy =0 with M = y (x+y) , My = x+2y N = x+2y-1 , Nx = 1. The equation is not exact but (My-Nx)/N =1,independent on y .The integrating factor is e^ (integral of 1dx) =e^x. Obtain the equation P (x,y)dx+ Q (x,y)dy =0 with NettetIn general, it turns out (see Theorem 4) that the two iterated integrals in Equations 2 and 3 are always equal; that is, the order of integration does not matter. (This is similar to Clairaut’s Theorem on the equality of the mixed partial derivatives.) ... dy ˜ y. 2 1 ˜ x. 3. 3. y ˚ x ˜0. x ˜3. dy ˜ ... Nettet23. mar. 2024 · Integrating Factors found by Inspection.1. y(2xy + 1)dx − xdy = 02. y(x^4 − y^2)dx + x (x^4 + y^ 4. 2) Suppose a beam whose one side is free and other side is fixed, ie a cantilever is subjected to a ; 5. A 2 kg mass is attached to a spring having spring constant 10 N/m. The mass is placed in a surroundi; 6. christian lauba