Determine the following integrals T Sin(x) 1 + x² dx 2). xe 2x dx Idy dx...
7. Evaluate the following integrals using integration by parts: a xe-ºrd sin (x)dx
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
solve the following differential equations (e* + 2y)dx + (2x – sin y)dy = 0 xy' + y = y? (6xy + cos2x)dx +(9x?y? +e")dy = 0 +2ye * )dx = (w*e * -2rcos x) di
Find f(x), assuming that f(x) ex dx = f(x) e' - 8x-1 ex dx. (Use C for the constant of integration.) Evaluate the integral. (Use C for the constant of integration.) cos 498(3y) sin?(3y) dy
Question 4 a) Differentiate with respect to x, i. y = sin 2x ii. y = x In(5x + 2) b) Show that if y = cotx, dy dx -cosec? x c) Show that if y = tan x, then dy dx 1 1+xal Question 5 Use calculus to find any turning points of the function A(t) = te-020 and determine their nature (maximum, minimum or inflexion) using any method. Question 6 a) Find tan” x dx b) Use integration...
(2x+ 2 x y²) dx + ( x ²) - 3y) dy = 0 solve your equation
Find an integrating factor of the form X"y" and solve the equation. (2x-172-9y)dx + (3y-6x) dy=0, y(1) =1 OA 4x2y3 – 3x3y2 = 1 08.3x2y3 – x3y2=2 ocx?y* - 3x4y2 = -2 D.*?y3 - 3x3y2=-2 Ex?y2 – 3x3y2 = -2
QUESTION 25 Find an integrating factor of the form x"y" and solve the equation. (2x+y2-9y)dx+ (3y-6x) dy=0; y(1) =1 A 4x2y3 – 3x3y2 = 1 o e x?y2-3x3y2 = -2 ocx?y* - 3x^y2=-2 02.3x2y3 – x3y2=2 Ex?y-3x?y2=-2
for differential equations 1. Identify each of the following differential equations as either Separable, Homogeneous, Linear Bernoulli, or Exact and solve the equation using the method of the type you have identified. Many can be classified in multiple ways, it is not necessary to list all possibilities. (3xy2 +2ycos x)+y'-y sin x-x =0 Туре: A. dx General Solution: B. (4xy+xy)2x+ xy2 dx Туре: General Solution: Туре: C. y'y'y+1 General Solution: (3x'y+e')-(2y-x-xe)dy Туре: D. dx General Solution: Туре: dy E. =y(xy-1)...
Question 2 (Learning Outcome 2) 0 S (*x+3) dx S A) Evaluate the following integrals. 4x+7 2x+5) 5x2–2x+3 (ii) dx (x2+1)(x-1) x2+x+2 (iii) S3x3 –x2+3x+1 dx dx (x+1)V-x-2x In (x) dx (iv) S x2 X+1 (vi) S dx (1+x2) (vii) S dx x(x+Inx) (viii) Stancos x) dx (ix) 30 Sin3 e*(1 + e*)1/2 dx dx 2 sin x cos x (x) S B) Find the length of an arc of the curve y =*+ *from x = 1 to x...