Arrington B11. (12 pts.) Let f(x) =2x1.(a) Approximate the area under the curve y = f(x) from a = 1 to b = 7 using a Riemannsum with 2 left rectangles. (Write the sum; you need not evaluate it.)(b) Find the exact value of the area under the curve y = f(x) from a = 1 to b = 7 by evaluating anappropriate definite integral using the Fundamental Theorem of Integral Calculus2. (15 pts.) Find the following integrals:(a) dx)1ex(x235(b)2x1xdx(c)131)xe( dxArrington B23. (14 pts.) Use substitution to find the following integrals:(a)xexdx(b)2183x2x3dx4. (6 pts.) Find the average value of f(x) =3xon [0,2].Arrington B35. (7 pts.) The acceleration of a particle at time t seconds is given by a(t) = 2t + 4e-0.2tft./sec2. Findv(t), the velocity of the particle at time t, if its initial velocity (the velocity at time t=0) is 5 ft/sec.6. (16 pts.) Set up, but do not evaluate, integrals for the area(a) Between the curves y = x3and y = x2from x = -1 to x = 1.(b) Bounded by the curves y = x and y = 4x –x2.Arrington B47. (6 pts.) Given a demand function of d(x) = 300 –0.4x and a supply function of s(x) = 0.2x.(a) Find the market demand (the positive value of x at which the demand function intersects thesupply function).(b) Set up, but do not evaluate a definite integral for the producers’ surplusat the market demand.8. (24 pts.) Use integration by parts to find:(a)xln dx(b)x3xe dx(c))xln(2dxArrington B5(5 pts) Extra-Credit : You may earn an extra 5 points by evaluating21dxxwithout using theFundamental Theorem of Calculus(10 pts) Extra-Credit : You may earn an extra 10 points by finding
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