7. [-/1.04 Points] DETAILS SCALCET9 5.2.040. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. (x 2 - 2x) dx (a) Find an approximation to the integral using a Riemann sum with right endpoints and n = 8. Rg = (b) Draw a diagram to illustrate the approximation in part (a). NWA UI N w NI NICI NIN NIN NICI 3 -1 3 -2 DO-3 -1 2 5 NIS NIC NI NI 5 2 -2- D-3 10-3 (c) Consider the following theorem. If f is integrable on [a, b], then ( f(x) dx = lim > f(x,) Ax, where Ax - B- 2 and x; = a + iAx. Use this to evaluate the integral. (d) Interpret the integral in part (c) as a difference of areas. The integral represents the area below the x-axis minus the area above the x-axis. The integral represents the area above the x-axis minus the area below the x-axis. Illustrate with a diagram. u a w L -2 N 2 Need Help? Read It8. [-/1.04 Points] DETAILS SCALCET9 5.2.036.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The graph of g consists of two straight lines and a semicircle as shown in the figure. 20 y = g(x) 10 X 0 20 35 Evaluate each integral by interpreting it in terms of areas. ( 10 (a) Jo 9 ( x) dx ( b ) 30 10 9 ( x ) dx ( C ) 3 9 (x) dx Need Help? Read It Master It 9. [-/1.04 Points] DETAILS SCALCET9 5.3.035. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral. 10 ( 4 + 8 ) ( 4 - 9 ) du Need Help? Read It Watch It 10. [-/1.04 Points] DETAILS SCALCET9 5.3.054. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral. [( x ) dx where (x ) = if - 4 5 x 5 0 1 16 - x 2 if 0