Clicker Question 1 What is the exact average value of f(x) = 1/x 2 between x = 1 and x = 3? – A. 1/3 – B. 2/3 – C. 2/9 – D. ln(3) – E. ln(3)/2

Clicker Question 2 What is the exact average height of the graph of g(x) = x sin(x 2 ) on the interval [0,  ]? – A. 2 – B. 2 /  – C. 1 /  – D. 1 – E. 

Areas between Curves (1/29/14) If two curves are described algebraically, we can use the definite integral to compute the area they enclose. It will be the integral of the upper curve minus the lower curve (by the Difference Rule). Watch out if they cross! We must, of course, find out where they intersect if no other boundaries are given.

Three Examples Find the exact area enclosed by f(x) = 2x – x 2 and g(x) = -3x. Find the exact area enclosed by the y-axis, the line y = e 2 and the curve y = e x. Find the area in the first quadrant enclosed by the line y = (1/e)x and the curve y = ln(x)?

Clicker Question 3 What is the exact area in the first quadrant enclosed by the axes and f (x) = 3 -  x ? – A. 9 sq. units – B. 9 – 2  3 sq. units – C. 12 sq. units – D. 10 1/3 sq. units – E. 18 sq. units

Assignment for Friday Read Section 6.1 On page 427, do Exercises 1, 5, 7, 9, 13, 15, 23 and 25.