FIGURE 17 13. Let f(x) = x². (a) Sketch the function over the interval [0,2] and the rectangles corre sponding to L4. Calculate the area contained within them. (b) Sketch the function over the interval [0,2] again but with the rect- angles corresponding to R4. Calculate the area contained within them. (e) Make a conclusion about the area under the curve f(x) = x² over the interval [0,2]. 14. Let f(x)=√√x. (a) Sketch the function over the interval [0,4] and the rectangles corre- sponding to L4. Calculate the area contained within them. (b) Sketch the function over the interval [0,4] again but with the rect- angles corresponding to R4. Calculate the area contained within them. (c) Make a conclusion about the area under the curve f(x)=√√x over the interval [0,4]. In Exercises 15-22, calculate the approximation for the given function and interval. 15. L4, f(x)=√√2-x, [0,2] 16. L6, f(x)=√√√6x+2, [1,3] 17. R6. f(x)=2x-x², [0,2] 18. R5, f(x) = x²+x, [-1,1] 19. Ms, f(x) Inx, [1,3] 20. M4, f(x)=2*, [1,3] 21. L4. f(x) = cos² x, [] 22. L6. f(x) = x²+3|x|, [-2,1] In Exercises 23-28, write the sum in summation notation. 23. 47 +57 +6 +77 +87 24. (2+2)+(3+3)+(42 +4)+(5²+5) 25. (22+2)+(23+2)+(24+2)+(25 +2) 26. 1+++++ 2 n 27. + ++ 2.3 (n+1)(n+2) +ex/n 28. e +e+ex/3+.... 29. Calculate the sums: 5 (2) Σ9 30. Calculate the sums: 5 (b) 4 (c) k=2