Answer Happy

1. Use the form of definition of the integral with xk∗​ as the right endpoint of each subinterval to find the area under the curve f(x)=x2+2x−5 and over the interval [1,4]. [6 marks] 2. Function f is defined as follows: f(x)=⎩⎨⎧​(x−2)2+3x+1x30​​,,,​0≤x≤33<x≤5x>5​ (a) Sketch the graph y=f(x). [2 marks] (b) The region R is bounded by the graph y=f(x), the y-axis, the lines x=2 and x=8. Find the area of the region R. [3 marks] (c) Determine the set values of x such that f(x)<31​x+3. [3 marks] 3. If fark​[p,q] denotes the average value of f on the interval [p,q] and p<k<q, show that fave​[p,q]=q−pk−p​favec​[p,k]+q−pq−k​fave​[k,q]