7.3 - Area Bounded by Curves and Axes
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Practice Questions
Test your understanding with targeted questions
Find the area under the curve \( y = x^3 \) from \( x = 0 \) to \( x = 1 \).
💡 Hint: Remember to integrate \\( x^3 \\).
Calculate the area under the curve \( y = 2x \) from \( x = 0 \) to \( x = 3 \).
💡 Hint: Integrate using basic power rule.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the formula to calculate the area bounded by a curve and the x-axis?
💡 Hint: Think about when a curve is below the x-axis.
True or False: The area between two curves is the integral of the upper function minus the lower function.
💡 Hint: Which function is on top?
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Challenge Problems
Push your limits with advanced challenges
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) \\).
Determine the area between the curves \( y = x^3 \) and \( y = -x \) from their points of intersection.
💡 Hint: Find the intersection points before integrating!
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