Sect 6.1 #11 | Summary and Q&A

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February 3, 2015
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blackpenredpen
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Sect 6.1 #11

TL;DR

This content explains how to find the area bounded by two sideway parabolas using integration.

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Questions & Answers

Q: How can you determine the orientation of a parabola based on its equation?

If the equation is a quadratic equation in terms of y, a negative coefficient in front of the y squared term indicates that the parabola will open to the left. A positive coefficient suggests it will open to the right.

Q: Why is it necessary to isolate the x-values in terms of y when finding the area?

Isolating the x-values allows us to express the curves as functions of y. Since the width of the rectangles used to calculate the area is the change in y, it is essential to have y as the independent variable.

Q: Why is it possible to write the integral as the right curve minus the left curve?

By subtracting the equation of the left curve from the right curve, we obtain the vertical height of the rectangles. This setup allows us to calculate the area bounded by the two curves.

Q: Can we use the power rule in reverse to integrate the expression?

Yes, by adding one to the exponent of y in the integral expression, we can apply the power rule in reverse. Dividing by the new exponent and integrating gives us the antiderivative of the expression.

Summary & Key Takeaways

  • The content discusses how to graph the parabolas by observing the equations and determining their orientation.

  • It explains that since the x-values are dependent on the y-values, the area should be calculated using horizontal rectangles.

  • The content demonstrates how to set up the integral using the right curve minus the left curve and integrate with respect to y.

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