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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the area under the curve y = x³ from x = 1 to x = 3.
💡 Hint: Calculate the integral of x³.
Question 2
Easy
Determine the area under y = 3x between x = 0 and x = 2.
💡 Hint: You need to integrate 3x from 0 to 2.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the definite integral calculate?
- Area under the curve
- Slope of the curve
- Intercept of the curve
💡 Hint: Think about what integration gives us regarding area.
Question 2
True or False: The area under the curve can be negative.
- True
- False
💡 Hint: Consider what happens when a curve is below the x-axis.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Calculate the area bounded by the curve y = x^3 and the line y = 2x, where they intersect.
💡 Hint: Make sure you calculate the definite integral properly after finding the intersection points.
Question 2
Determine the area under the curve y = e^(-x^2) from x = -∞ to x = +∞.
💡 Hint: Think about symmetry in the limits and properties of e^(-x^2).
Challenge and get performance evaluation