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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 \( y = x^3 \) from \( x = 0 \) to \( x = 1 \).
💡 Hint: Remember to integrate \\( x^3 \\).
Question 2
Easy
Calculate the area under the curve \( y = 2x \) from \( x = 0 \) to \( x = 3 \).
💡 Hint: Integrate using basic power rule.
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 is the formula to calculate the area bounded by a curve and the x-axis?
- \\( \\int_a^b f(x) \\
- dx \\)
- \\( \\int_a^b |f(x)| \\
- dx \\)
- \\( |f(x)| \\
- dx \\)
💡 Hint: Think about when a curve is below the x-axis.
Question 2
True or False: The area between two curves is the integral of the upper function minus the lower function.
- True
- False
💡 Hint: Which function is on top?
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the area bounded by the curve \( y = \ln(x) \), the x-axis, and the lines \( x = 1 \) and \( x = e \).
💡 Hint: Use integration by parts for \\( \\ln(x) \\).
Question 2
Determine the area between the curves \( y = x^3 \) and \( y = -x \) from their points of intersection.
💡 Hint: Find the intersection points before integrating!
Challenge and get performance evaluation