1. More Definite Integrals
TS: Explicitly assessing information and drawing conclusions

2. Objectives
To evaluate definite integrals.

3. The Fundamental Theorem of Calculus
So this would represent
the area between the curve
y = 3 and the
x-axis from x = 2 to 7

4. The Fundamental Theorem of Calculus
So this would represent
the area between the curve
y = x+4 and the
x-axis from x = 0 to 2

5. The Fundamental Theorem of Calculus
Substitute into
the integral.
Always express your
answer in terms of the
original variable.

6. The Fundamental Theorem of Calculus
So this would represent
the area between the curve
y = (x+1)/(x2+2x-3) and the
x-axis from x = 2 to 3

7. Conclusion
A function and the equation for the area between its graph and the x-axis are related to each other by the antiderivative.
The Fundamental Theorem of Calculus enables us to evaluate definite integrals. This empowers us to find the area between a curve and the x-axis.