Signed Area (VCE SSCE Mathematical Methods): Quizzes

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Signed area
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What does signed area account for that total area does not?

Position relative to xx-axis

What sign does a region below the xx-axis have for signed area?

Negative

What does the definite integral abf(x)dx\int_a^b f(x)\,dx give?

Signed area

If f(x)0f(x) \leq 0 for all x[a,b]x \in [a,b], what is the area formula?

abf(x)dx-\int_a^b f(x)\,dx

If f(x)0f(x) \geq 0 for all x[a,b]x \in [a,b], what is the area formula?

abf(x)dx\int_a^b f(x)\,dx

What does 31f(x)dx\int_3^1 f(x)\,dx equal?

13f(x)dx-\int_1^3 f(x)\,dx

What does ab5f(x)dx\int_a^b 5f(x)\,dx equal?

5abf(x)dx5\int_a^b f(x)\,dx

What does 22f(x)dx\int_2^2 f(x)\,dx equal?

00

For signed area of 4 regions, if A1,A3A_1, A_3 are above and A2,A4A_2, A_4 below, what is the formula?

A1A2+A3A4A_1 - A_2 + A_3 - A_4

What is most important to consider when finding area enclosed by y=f(x)y = f(x)?

Sign of f(x)f(x) in the interval

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