Clicker Question 1
What is the exact average value of f(x) = 1/x2between 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 graphof g(x) = x sin(x2) 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, wecan use the definite integral to compute thearea they enclose.
It will be the integral of the upper curve minusthe lower curve (by the Difference Rule).Watch out if they cross!
We must, of course, find out where theyintersect if no other boundaries are given.
Three Examples
Find the exact area enclosed byf(x) = 2x – x2 and g(x) = -3x .
Find the exact area enclosed by the y-axis,the line y = e2 and the curve y = ex .
Find the area in the first quadrant enclosedby the line y = (1/e)x and the curve y = ln(x)?
Clicker Question 3
What is the exact area in the first quadrantenclosed by the axes and f (x) = 3 - x ?
–A. 9 sq. units
–B. 9 – 23 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.