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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the area between the line y = 2 and the curve y = x².
💡 Hint: Remember to square y when finding the area under the curve.
Question 2
Easy
Calculate the area between the curves x = y³ and x = 1.
💡 Hint: Estimate the integral values to find the exact area.
Practice 1 more question 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 for finding the area in terms of the y-axis?
- A = ∫ f(x) dx
- A = ∫ f(y) dy
- A = f(y) dy
💡 Hint: Think about how the integrations are adjusted according to the axis in question.
Question 2
Is A = ∫ from y=c to y=d f(y) dy applicable for determining area under curves?
- True
- False
💡 Hint: Recall that integration requires limits.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the area between the curves y = e^y and y = y² from y = 0 to y = 2.
💡 Hint: Consider the shape formed by the curves to accurately decide the integration order.
Question 2
Determine the area under the curve defined as x = y³ from y = 1 to y = 3.
💡 Hint: Sketch the area for better visualization.
Challenge and get performance evaluation