Practice Solved Examples - 7.5 | 7. Applications of Integrals | ICSE 12 Mathematics
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7.5 - Solved Examples

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Find the area under the curve y = x³ from x = 1 to x = 3.

💡 Hint: Calculate the integral of x³.

Question 2 Easy

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

Question 1

What does the definite integral calculate?

Area under the curve
Slope of the curve
Intercept of the curve

💡 Hint: Think about what integration gives us regarding area.

Question 2

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

True
False

💡 Hint: Consider what happens when a curve is below the x-axis.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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