Area between 2 curves (Edexcel A-Level Mathematics): Quizzes

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Area between 2 curves
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What is the alternative method for area between curves y=f(x)y = f(x) and y=g(x)y = g(x)?

∫(f(x)−g(x)) dx\int (f(x) - g(x)) \, dx

What is the formula for area between a curve and the yy-axis?

∫y1y2x dy\int_{y_1}^{y_2} x \, dy

What is the area between y=x2y = x^2 and y=x3y = x^3 from x=0x = 0 to x=1x = 1?

112\frac{1}{12}

What is the first step to find area between a curve and the yy-axis?

Rearrange equation to x=f(y)x = f(y)

For y=x2y = x^2, what is xx in terms of yy in the positive quadrant?

x=yx = \sqrt{y}

For y=x3y = x^3 with x=2x = 2 to x=3x = 3, what are the yy-limits?

y=8y = 8 to y=27y = 27

What is ∫827y13 dy\int_8^{27} y^{\frac{1}{3}} \, dy equal to?

1954\frac{195}{4}

What is the area between y=x2+1y = x^2 + 1 and y=11−9x2y = 11 - \frac{9}{x^2} from x=1x = 1 to x=3x = 3?

163\frac{16}{3}

When finding complex areas, what should you be careful about?

Area not contained above & below by curves

What is ∫57(y2−6y+7) dy\int_5^7 (y^2 - 6y + 7) \, dy equal to?

443\frac{44}{3}

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