Practice Practice Exercise (7.6) - Applications of Integrals - ICSE 12 Mathematics

Practice: Practice Exercise

Lesson 7.6Applications of Integrals

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Find the area under the curve $y = 2x$ from $x = 0$ to $x = 3$ .
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Use the area under the curve formula!
Question 2.
Calculate the area between the x-axis and the curve $y = 3$ from $x = 1$ to $x = 4$ .
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Remember the area is constant here!
3Question 3.
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} \$
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Remember, it's integral notation!
4Question 4.
The area between two curves is computed using which formula?
- True
- False
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Think about the curves in relation to each other.
Question 5.
Determine the area between the curves $y = x^3 - 6x$ and the x-axis over the interval $[-2, 2]$ .
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Use the first derivative to find local maxima and minima.
Question 6.
Calculate the area enclosed between the curves $y = \sin^2(x)$ and $y = 1 - \sin(x)$ over the interval $[0, 2\pi]$ .
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Check where the sin functions intersect; that will guide your integration sums.

4 more questions in this section. Enroll free to practise them all.