The Fundamental Theorem of Calculus

1
The Fundamental Theorem of Calculus

• Yes, it really is this easy!

2
First Fundamental Theorem

• Take the Antiderivative.
• Evaluate the Antiderivative
• at the Upper Bound.
• Evaluate the Antiderivative
• at the Lower Bound.
• Subtract the Lower Bound Value
• from the Upper Bound Value.

3
AREA under f (x)
down to the x-axis
from x a to x b

• Use your graphing calculator to graph
  the integrand
• and determine whether the integral
  is
• positive, negative, or zero.

4
Evaluate Definite Integralswith your calculator.

• Enter the function in y .
• GRAPH CALC (2nd TRACE) ? Option 7
• or MATH ? Option 9 fnInt(y1,x, __,
  __)
• Enter Lower Bound
• Enter Upper Bound

5
Evaluate the Definite Integral.Use your
calculator to check.
6
Evaluate the Definite Integral.Use your
calculator to check.
7
Evaluate the Definite Integral.Use your
calculator to check.
8
Evaluate the Definite Integral.Use your
calculator to check.
9
Evaluate the Definite Integral.Use your
calculator to check.
10
Find the AREA of the region bounded by