More Definite Integrals

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Presentation transcript:

More Definite Integrals TS: Explicitly assessing information and drawing conclusions

Objectives To evaluate definite integrals.

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

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

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

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

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.