Practice Area Under a Curve - 7.1 | 7. Applications of Integrals | ICSE 12 Mathematics
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Area Under a Curve

7.1 - Area Under a Curve

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the area under the curve y = 3x from x = 0 to x = 2?

💡 Hint: Use the definite integral to calculate.

Question 2 Easy

How do you express the area under y = x² from x = a to x = b?

💡 Hint: Remember the formula for definite integrals.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the definite integral \( \int_a^b f(x) \, dx \) represent?

The slope of the function
The area under the curve
The average value of the function

💡 Hint: Think about what an integral accumulates over an interval.

Question 2

True or False: The area found under a curve can be negative.

True
False

💡 Hint: Remember the definition of signed area.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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