7.1 - Area Under a Curve
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Practice Questions
Test your understanding with targeted questions
What is the area under the curve y = 3x from x = 0 to x = 2?
💡 Hint: Use the definite integral to calculate.
How do you express the area under y = x² from x = a to x = b?
💡 Hint: Remember the formula for definite integrals.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the definite integral \( \int_a^b f(x) \, dx \) represent?
💡 Hint: Think about what an integral accumulates over an interval.
True or False: The area found under a curve can be negative.
💡 Hint: Remember the definition of signed area.
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Challenge Problems
Push your limits with advanced challenges
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?
💡 Hint: Consider the points of intersection for better understanding.
Determine the area between the curve of y = x² + 1 and the x-axis from x = -1 to x = 1.
💡 Hint: Sketch the graph to visualize areas effectively.
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