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

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Area between 2 curves
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What is the method to find area between two curves from x=ax=a to x=bx=b?

Subtract lower curve area from upper

What is the alternative to finding areas separately then subtracting?

Integrate (f(x)−g(x))(f(x) - g(x)) directly

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

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

What is ∫01(x2−x3)dx\int_0^1 (x^2 - x^3) dx?

112\frac{1}{12}

When finding area with the yy-axis, what limits should you use?

y-limits, not x-limits

For y=3+x+2y = 3 + \sqrt{x+2}, when x=2x=2, what is yy?

55

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}

Rearranging y=3+x+2y = 3 + \sqrt{x+2} to find xx gives:

x=y2−6y+7x = y^2 - 6y + 7

What must you do when area is not contained from above and below by two curves?

Split into separate regions

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