Practice Area In Terms Of Y-axis (7.4) - Applications of Integrals

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6 sample questions

Question 1.
Find the area between the line y = 2 and the curve y = x².
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Remember to square y when finding the area under the curve.
Question 2.
Calculate the area between the curves x = y³ and x = 1.
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Estimate the integral values to find the exact area.
3Question 3.
What is the formula for finding the area in terms of the y-axis?
- A = ∫ f(x) dx
- A = ∫ f(y) dy
- A = f(y) dy
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Think about how the integrations are adjusted according to the axis in question.
4Question 4.
Is A = ∫ from y=c to y=d f(y) dy applicable for determining area under curves?
- True
- False
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Recall that integration requires limits.
Question 5.
Find the area between the curves y = e^y and y = y² from y = 0 to y = 2.
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Consider the shape formed by the curves to accurately decide the integration order.
Question 6.
Determine the area under the curve defined as x = y³ from y = 1 to y = 3.
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Sketch the area for better visualization.

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