Practice Practice Exercise - 7.6 | 7. Applications of Integrals | ICSE 12 Mathematics
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Practice Exercise

7.6 - Practice Exercise

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Learning

Practice Questions

Test your understanding with targeted questions

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!

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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