Last updated on Sep 20, 2026

Signed Area (VCE SSCE Mathematical Methods): Flashcards

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Sum of all regions regardless of position relative to $x$ -axis

Area accounting for regions above (+) and below (-) $x$ -axis

Signed area, not total area

$\int_a^b f(x)dx$

$-\int_a^b f(x)dx$

Integral gives negative value; area must be positive

Reversing limits property

$k\int_a^b f(x)dx$

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Explore VCE SSCE Mathematical Methods Model Answers by Topics

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Explore VCE SSCE Mathematical Methods Exam Questions by Topics

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Signed Area (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

Total area definition

Signed area definition

Sign of area above xxx-axis

Sign of area below xxx-axis

What does ∫abf(x)dx\int_a^b f(x)dx∫ab​f(x)dx give?

Area when f(x)≥0f(x) \geq 0f(x)≥0 on [a,b][a,b][a,b]

Area when f(x)≤0f(x) \leq 0f(x)≤0 on [a,b][a,b][a,b]

Why negate integral when f(x)≤0f(x) \leq 0f(x)≤0?

∫abf(x)dx=−∫baf(x)dx\int_a^b f(x)dx = -\int_b^a f(x)dx∫ab​f(x)dx=−∫ba​f(x)dx

∫abkf(x)dx\int_a^b kf(x)dx∫ab​kf(x)dx

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Estimating the Area Under a Graph

Antidifferentiation: Indefinite Integrals

Two Antiderivatives

The Fundamental Theorem of Calculus and the Definite Integral

Finding the Area Under a Curve

Integration of Circular Functions

Miscellaneous Exercises

Signed Area

The Area of a Region Between Two Curves

Applications of Integration

The Area of a Region Between Two Curves

Applications of Integration

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Estimating the Area Under a Graph

Antidifferentiation: Indefinite Integrals

Two Antiderivatives

The Fundamental Theorem of Calculus and the Definite Integral

Finding the Area Under a Curve

Integration of Circular Functions

Miscellaneous Exercises

Signed Area

The Area of a Region Between Two Curves

Applications of Integration

The Area of a Region Between Two Curves

Applications of Integration

Explore VCE SSCE Mathematical Methods Quizzes by Topics

Estimating the Area Under a Graph

Antidifferentiation: Indefinite Integrals

Two Antiderivatives

The Fundamental Theorem of Calculus and the Definite Integral

Finding the Area Under a Curve

Integration of Circular Functions

Miscellaneous Exercises

Signed Area

The Area of a Region Between Two Curves

Applications of Integration

The Area of a Region Between Two Curves

Applications of Integration

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

Estimating the Area Under a Graph

Antidifferentiation: Indefinite Integrals

Two Antiderivatives

The Fundamental Theorem of Calculus and the Definite Integral

Finding the Area Under a Curve

Integration of Circular Functions

Miscellaneous Exercises

Signed Area

The Area of a Region Between Two Curves

Applications of Integration

The Area of a Region Between Two Curves

Applications of Integration

Join 100,000+ SSCE students studying Flashcards with us.

Sign of area above $x$ -axis

Sign of area below $x$ -axis

What does $\int_a^b f(x)dx$ give?

Area when $f(x) \geq 0$ on $[a,b]$

Area when $f(x) \leq 0$ on $[a,b]$

Why negate integral when $f(x) \leq 0$ ?

$\int_a^b f(x)dx = -\int_b^a f(x)dx$

$\int_a^b kf(x)dx$