Area between a curve and a line (AQA A-Level Mathematics): Quizzes

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Area between a curve and a line
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What is the first step to find the area between a curve and a line?

Find points of intersection

What equation do you solve to find where y=f(x)y = f(x) and y=g(x)y = g(x) intersect?

f(x)=g(x)f(x) = g(x)

What is the general formula for area between curve and line from x=ax = a to x=bx = b?

∫ab∣f(x)−g(x)∣dx\int_a^b |f(x) - g(x)| dx

When can the absolute value be omitted from ∫ab∣f(x)−g(x)∣dx\int_a^b |f(x) - g(x)| dx?

When f(x)≥g(x)f(x) \geq g(x) over interval

What must you do if the functions cross each other within the interval?

Split integral at crossing point(s)

To find where y=x2y = x^2 and y=x+2y = x + 2 intersect, which equation do you solve?

x2=x+2x^2 = x + 2

What are the solutions to (x−2)(x+1)=0(x - 2)(x + 1) = 0?

x=2x = 2 and x=−1x = -1

For y=x2y = x^2 and y=x+2y = x + 2 on [−1,2][-1, 2], which function is greater?

x+2x + 2

What is the antiderivative of x+2−x2x + 2 - x^2?

x22+2x−x33+C\frac{x^2}{2} + 2x - \frac{x^3}{3} + C

What is the area between y=x2y = x^2 and y=x+2y = x + 2 from x=−1x = -1 to x=2x = 2?

92\frac{9}{2} square units

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