More Definite Integrals

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 x4 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 (x1)/(x22x-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.