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More Definite Integrals
TS: Explicitly assessing information and drawing conclusions
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Objectives To evaluate definite integrals.
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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
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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
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The Fundamental Theorem of Calculus
Substitute into the integral. Always express your answer in terms of the original variable.
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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
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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.
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