Application of Integrals - Class XII Mathematics Quiz
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Preview questions
1. What is the area under the curve y = f(x) from x = a to x = b?
f(b) - f(a) · ∫[a to b] f(x) dx · b - a · f(a) + f(b)
2. The integral ∫[0 to 1] (x^2 + 2x) dx represents what?
The area under the curve from 0 to 1 · The volume of a solid · The length of the curve · The average value of the function
3. Which of the following is used to find the area between two curves?
∫[a to b] (f(x) - g(x)) dx · ∫[a to b] f(x) dx + ∫[a to b] g(x) dx · f(b) - f(a) · ∫[a to b] f(x) dx * g(x)
4. To find the area bounded by the x-axis and the curve y = x^3 from x = 0 to x = 2, we compute:
∫[0 to 2] x^3 dx · ∫[0 to 2] 3x^2 dx · ∫[0 to 2] x^2 dx · ∫[0 to 2] 2x^3 dx
5. What is the formula for the area of a region bounded by the curve y = f(x) and the x-axis?
∫ f(x) dx · ∫[a to b] |f(x)| dx · ∫[a to b] f(x) dx · f(b) - f(a)
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