Practice Area Under A Curve (7.1) - Applications of Integrals

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8 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the area under the curve y = 3x from x = 0 to x = 2?
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Use the definite integral to calculate.
Question 2.
How do you express the area under y = x² from x = a to x = b?
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Remember the formula for definite integrals.
3Question 3.
What does the definite integral $\int_a^b f(x) \, dx$ represent?
- The slope of the function
- The area under the curve
- The average value of the function
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Think about what an integral accumulates over an interval.
4Question 4.
True or False: The area found under a curve can be negative.
- True
- False
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Remember the definition of signed area.
Question 5.
A function has an area calculated by the integral $\int_{1}^{5} 2x - 3 \, dx$ . What is the area between the curve and the x-axis, considering signed areas?
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Consider the points of intersection for better understanding.
Question 6.
Determine the area between the curve of y = x² + 1 and the x-axis from x = -1 to x = 1.
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Sketch the graph to visualize areas effectively.

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