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Evaluate the integral 5*7* (sins 2x)(cos 2x) dx by substitution method.
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
Consider the figure below. f(x) = 2x – x2 g(x) = x2 - 6x 81x) -10 (a) For the shaded region, find the points of intersection of the curves. (x, y) = ( 0,0 ) (smaller x-value) (x, y) = ( 4,-8 ) (larger x-value) (b) Form the integral that represents the area of the shaded region. dx (c) Find the area of the shaded region.
Do not use calculator. 10 2. The value of " do is to s'of?dx = 5"x"dx = * | - x - - - - - 105 - - - 3. Find ((2 +6)(2 – 2)de 3 +2x?-12x+C 5(X+6)(x-2)dx =S(X?-2x +6x–12 )dx =5x+4y-tzdy = x + -12y = x+2x?_12y+C Math 148 Business Calculus Page 1
18. Is the function f(x) = 6x + 2x + 7 even, odd, or neither?
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
Sa. sec(ax) •dx Va? - tan(ax) 5b. 35 (Ine)? dx 25 + (inverse trig functions) 7. The split method 6. Extended substitution 2x + 7 ſsin 2x \sin x – 3 dx •dx r? +6x +10 (5 points) 3x + 7 y 8. (5 points) Find the equation of a line that is tangent to a cure 2x+3 at (1,2). Leave the answer in the slope and y-intercept form as y = mx+b. No need to graph any picture at...
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 22 Find an integrating factor of the form X"y" and solve the equation. (2x+4y2-9y)dx+ (3y-6x) dy=0, y (1) =1 O A *?y2 – 3x3y2 = -2 08.x2y4 – 3x4y2 = -2 oc 3x²y3 – x3y2=2 00.x2y3–3x3y2=-2 o e 4x2y3 – 3x3y2 = 1
Evaluate the following integral. + 6x - 1 dx X-X Find the partial fraction decomposition of the integrand. St*6x=1&x=SO dx Evaluate the indefinite integral. S*** + 6x - 1 3 X-X dx =