Practice Summary (7.7) - Applications of Integrals

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Find the area under the curve y = 3x from x = 0 to x = 2.
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Use the power rule for integration.
Question 2.
Calculate the area between y = 2x and y = x^2 from x = 0 to x = 2.
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Find intersection points if any before integrating.
3Question 3.
What does the definite integral measure?
- Only area under the curve
- Net area under the curve
- Perimeter
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Think about the area it calculates.
4Question 4.
True or False: The area between two curves can be negative.
- True
- False
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Consider the definition of area.
Question 5.
Calculate the area of the region enclosed by the curve y = x^3 and the line y = 3x from x = -1 to x = 2.
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First, find the intersection points to set your limits.
Question 6.
Determine the area between y = ln(x) and y = 1 from x = e to x = e^2.
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Identify the integration limits accurately.

5 more questions in this section. Enroll free to practise them all.