7.5 - Solved Examples
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Practice Questions
Test your understanding with targeted questions
Find the area under the curve y = x³ from x = 1 to x = 3.
💡 Hint: Calculate the integral of x³.
Determine the area under y = 3x between x = 0 and x = 2.
💡 Hint: You need to integrate 3x from 0 to 2.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the definite integral calculate?
💡 Hint: Think about what integration gives us regarding area.
True or False: The area under the curve can be negative.
💡 Hint: Consider what happens when a curve is below the x-axis.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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).
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