Practice Applications Of Integrals (7) - Applications of Integrals

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6 sample questions

Question 1.
Find the area under the curve y = 2x from x = 1 to x = 3.
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Apply the definite integral formula.
Question 2.
What is the area under the curve y = 3 from x = 0 to x = 4?
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Constant functions have a simple integration.
3Question 3.
What does the definite integral of a function represent?
- Area under the curve
- Slope of the curve
- Distance covered
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Think about what integrates calculate.
4Question 4.
True or False: The area under a curve can be negative.
- True
- False
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Remember the concept of signed areas.
Question 5.
A region is bounded by y = 4 - x² and the x-axis. Find the area of this region.
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Sketch the curve and determine your limits.
Question 6.
Evaluate the area enclosed between the curves y = e^x and y = e^-x from x = -1 to x = 1.
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Factor out the constants after solving the integral.

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