Practice Area Bounded by Curves and Axes - 7.3 | 7. Applications of Integrals | ICSE 12 Mathematics
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Area Bounded by Curves and Axes

7.3 - Area Bounded by Curves and Axes

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Find the area under the curve \( y = x^3 \) from \( x = 0 \) to \( x = 1 \).

💡 Hint: Remember to integrate \\( x^3 \\).

Question 2 Easy

Calculate the area under the curve \( y = 2x \) from \( x = 0 \) to \( x = 3 \).

💡 Hint: Integrate using basic power rule.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula to calculate the area bounded by a curve and the x-axis?

\\( \\int_a^b f(x) \\
dx \\)
\\( \\int_a^b |f(x)| \\
dx \\)
\\( |f(x)| \\
dx \\)

💡 Hint: Think about when a curve is below the x-axis.

Question 2

True or False: The area between two curves is the integral of the upper function minus the lower function.

True
False

💡 Hint: Which function is on top?

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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) \\).

Challenge 2 Hard

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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