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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 \( y = 2x \) from \( x = 0 \) to \( x = 3 \).
💡 Hint: Use the area under the curve formula!
Question 2
Easy
Calculate the area between the x-axis and the curve \( y = 3 \) from \( x = 1 \) to \( x = 4 \).
💡 Hint: Remember the area is constant here!
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 find the area under a curve?
- \\( \\int_a^b f(x) \\
- dx \\)
- \\( f(x) + C \\)
- \\( \\frac{f(b) - f(a)}{b-a} \\)
💡 Hint: Remember, it's integral notation!
Question 2
The area between two curves is computed using which formula?
- True
- False
💡 Hint: Think about the curves in relation to each other.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Determine the area between the curves \( y = x^3 - 6x \) and the x-axis over the interval \([-2, 2]\).
💡 Hint: Use the first derivative to find local maxima and minima.
Question 2
Calculate the area enclosed between the curves \( y = \sin^2(x) \) and \( y = 1 - \sin(x) \) over the interval \([0, 2\pi]\).
💡 Hint: Check where the sin functions intersect; that will guide your integration sums.
Challenge and get performance evaluation