Math 205 Midterm
Math 205 Midterm Click Link Below To Buy: http://hwcampus.com/shop/math-205-midterm-test/ Contact Us: [email protected] 1. (5 marks): (a) Approximate the de nite integral A = 3 R approximating rectangles of equal widths. Riemann sum 3 using 3 R (b)Now nd the approximation by a left Riemann sum L3, again using 3 approximating rectangles of equal widths. (c)Calculate the exact value of A by integrating. Comparing this value with 12 (R3 + L3) : Do your results found in (a) and (b) appear reasonably accurate? 2. (3 marks): (a) Use Part 1 of the Fundamental Theorem of Calculus to nd F0(x) 3 p dt. for F(x) = cos x 1 + t3 R 10t 3. (5 marks): Find f(t); given f0(t) = p3 and f(8) = 20. t 2 4. (10 marks): Calculate the following inde nite integrals Z p x3 Z 3 x2 + 4x + 4 (a) dx (b) dx x3 + x 16 x2 5. (12 marks): Evaluate the following de nite integrals (do not approximate): e (a) Z0 cos4 x tan2 x dx (b) Z1 x2 ln xdx 6. (5 marks): Find the area of the region enclosed by the curves x = jyj and x = y2 2. Bonus. (2 marks): Given that Z [f (x) + f00 (x)] sin xdx = 2 0 and f ( ) = 1; nd f (0).
