http://webspace.ship.edu/msrenault/geogebracalculus/integration_riemann_sum.html

(a) (part 1) Consider the function f (a) = -0.3x2 +6 from x = 1 to x = 4. Use left-hand and right-hand sums with 6 divisions (n = 6) to approximate the area between the function and x-axis from x = 1 to x = 4. Draw and accurate graph to show each of these sums. (b) ((Part 2) Use the Geogebra app: http://webspace. ship. edu/msrenault/geogebra.calculus/ integration_riemann_sum. html to answer these questions. i. Use the app to find the value of sin(2x) - 7 3 10 +3 dx. Explain what this number represents. 2 2 ii. Explain why sin(2x) + 3 ) dx is negative. 5 10 iii. Show that 1.' ( sin( 20) - 2-2 10 +3) dx + sin(2x)- 10 +3) dx = sin ( 2x) - 10 +3 dx