Evaluate the following 1+ y2 (1 + x2)xy Evaluate dy dr ' Sear²dx ſ 2 sec(3.c)dc
5. Evaluate the integral sec" x dr. 6. Evaluate the integral I 2 dx X3 V x2 – 1 >1. 7. Evaluate the integral dc I VAI 8. Evaluate the integral 19 - 22 dc. .x2
Evaluate the iterated integral. 12 [[(x2 - y2) dy dx J-13-2
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
Q1: Change the order of integration 1 rx-2 61 xy dy dx xy dy dx Jo x2 Evaluate the reversed integral and sketch the region.
5) Use Green's Theorem to evaluate | (xy)dx + (y2 +4)dy where is the cardoid r = 1 + sine OSOS 21 с
1&2 1. Find dy/dx for the curve r + xy + y2 = 3. 2. Use local linearization to estimate V29. Leave your answer as a simplified fraction.
Calculus 3 Evaluate SOLVE NUMBER 30 Evaluate x2 dx dy (x + 4y3) dx dy x + 4y dx dy cos(2x + y) dy dx e-3x-4y dy dx
dy dx Find when x = 3 and = -2, given that x2 + y2 = 35. dt dt dy (Round to two decimal places as needed.)
2. Convert to cylindrical coordinates. Do not evaluate. V5 10-22-y2 cos(.x2 + y²) dz dx dy. 22+y?
Solve 1st order non-linear differential equation by Bernoulli's equation x2 dy/dx + y2 = xy Kindly simplify every step, thanks!