Last updated on Sep 20, 2026

Applications of Integration (VCE SSCE Mathematical Methods): Quizzes

Applications of Integration

Practise the questions

10 questions from this quiz

$\frac{1}{b-a}\int_a^b f(x)\,dx$

Height of rectangle with same area as curve

$\frac{4}{3}$

Works backwards to find total change

Straight line through $(30,0)$

$\frac{-2}{T-30}$

$5.78$ minutes

Time for temperature change

Time per degree of temperature change

Total area under the curve

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Explore VCE SSCE Mathematical Methods Flashcards by Topics

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

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Applications of Integration (VCE SSCE Mathematical Methods): Quizzes

Practise the questions

What is the formula for the average value of fff over interval [a,b][a,b][a,b]?

What does the average value of a function represent geometrically?

For f(x)=x2f(x) = x^2f(x)=x2 on [0,2][0,2][0,2], what is the average value?

What does integration do when working with rates of change?

For dTdt=−0.5(T−30)\frac{dT}{dt} = -0.5(T-30)dtdT​=−0.5(T−30), what type of graph is dTdt\frac{dT}{dt}dtdT​ vs TTT?

If dTdt=−0.5(T−30)\frac{dT}{dt} = -0.5(T-30)dtdT​=−0.5(T−30), what is dtdT\frac{dt}{dT}dTdt​?

What is the area under dtdT\frac{dt}{dT}dTdt​ from T=35T=35T=35 to T=120T=120T=120 in the cooling example?

What does the area under a dtdT\frac{dt}{dT}dTdt​ curve represent?

What does dtdT\frac{dt}{dT}dTdt​ tell us in the cooling problem?

In the average value formula, what does ∫abf(x) dx\int_a^b f(x)\,dx∫ab​f(x)dx represent?

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 Flashcards 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 Quizzes with us.

What is the formula for the average value of $f$ over interval $[a,b]$ ?

For $f(x) = x^2$ on $[0,2]$ , what is the average value?

For $\frac{dT}{dt} = -0.5(T-30)$ , what type of graph is $\frac{dT}{dt}$ vs $T$ ?

If $\frac{dT}{dt} = -0.5(T-30)$ , what is $\frac{dt}{dT}$ ?

What is the area under $\frac{dt}{dT}$ from $T=35$ to $T=120$ in the cooling example?

What does the area under a $\frac{dt}{dT}$ curve represent?

What does $\frac{dt}{dT}$ tell us in the cooling problem?

In the average value formula, what does $\int_a^b f(x)\,dx$ represent?