MA 241 Calculus 1 Spring 2024 Practice for Test 4 10. Express each of the following sums in sigma notation. (There is more than 1 correct answer. Only 2 of the possibilities are provided on the answer key.) a. 1+4+16+64 + 256 d. 1-3+9-27+81 b. -5+25-125 + 625-3125 c. 3+5+7+9+11+13 e. 3+ 4+ 5+ 6+7+8 11. Find the derivatives. d dx a. fsint dt b. sint 1 du dt 0 4-u C. *cos t dt 12. Evaluate the integral. (Give the answers as exact values.) a. (-) dy d. fln2 e 3x dx g. ft (1+ t)7 dt b. f/2 16 sint dt e. f 7x(x-6)dx c. 3/2 18 cos 0 de f. /sec 0 de 13. Find the average value of the function over the given interval. (Give the answer as exact values.) a. y = 5 x; [-1,1] b. f(t)=(t-7)3; [0,12] 14. Find the total area of the shaded region. (Practice using calculus methods and showing organized work.) 6- y=2x+1 4. (1,3) 2- 0 a. (3,7) 3 -3 +2 x 2 MA 241 Calculus 1 Practice for Test 4 Spring 2024 16 (3,15) 12 -8- y=x-4x + 1 (0,0) N b. c. Between y = 9-x and the x-axis over the interval [0,5] 1 d. Between y = and the x-axis over the interval from [2,6] I