5.3 Fundamental Theorem of
Calculus Part 1
Thurs Nov 17
• Do Now
• Use geometry to compute the area
represented by the integral
3
ò (2x + 4)dx
-2
HW Review
The Fundamental Theorem of Calculus
Part 1
• Assume that f(x) is continuous on [a,b], then
ò
b
a
f '(x)dx = f (b) - f (a)
• f(b) – f(a) is considered to be the total change
(net change) or accumulation of the function
during the interval [a,b]
Notes about FTC1
• Notation:
b
f (b) - f (a) = f (x) a
• There’s a calculator function allowed on the
AP exam which we will use until we learn
faster ways to evaluate integrals
Ex
• Calculate the area under the graph of
f(x) = x^3 over [2,4]
• fnInt(x^3,x,2,4)
Ex
• Find the area under g(x) =
over the interval [1,3]
x
-3/4
+ 3x
5/3
Ex
• Find the area under f(x) = sinx on the intervals
[0, pi] and [0, 2pi]
Closure
• Find the area under the function f(x) = 1/x on
the intervals [2,8] and [-10,-4]
• HW: p. 314 #5 17 25 37 45 55