Area Under a Curve (Edexcel A-Level Mathematics): Quizzes

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Area Under a Curve
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What formula represents the area under curve y=f(x)y = f(x) from x=ax = a to x=bx = b?

∫abf(x) dx\int_a^b f(x) \, dx

If f(x)≥0f(x) \geq 0 for all xx in [a,b][a, b], what does ∫abf(x) dx\int_a^b f(x) \, dx give?

Total area under curve above x-axis

What does the definite integral compute when f(x)f(x) crosses the x-axis?

Net area (positive minus negative)

What is ∫02x2 dx\int_0^2 x^2 \, dx equal to?

83\frac{8}{3}

What is ∫0πsin⁡(x) dx\int_0^\pi \sin(x) \, dx equal to?

22

If curve lies below x-axis, how do you find the actual area?

Take absolute value of the integral

Formula for area between y=f(x)y = f(x) and y=g(x)y = g(x) where f(x)≥g(x)f(x) \geq g(x) on [a,b][a, b]?

∫ab[f(x)−g(x)] dx\int_a^b [f(x) - g(x)] \, dx

What should you do when a curve crosses the x-axis to find total area?

Integrate separately & use absolute values

What does ∣x∣|x| represent?

Modulus/magnitude/distance from 00

Area between y=x2y = x^2 and y=x+2y = x + 2 from x=0x = 0 to x=1x = 1 is?

136\frac{13}{6}

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