Last updated on Sep 20, 2026

The Area of a Region Between Two Curves (VCE SSCE Mathematical Methods): Quizzes

The Area of a Region Between Two Curves

Practise the questions

10 questions from this quiz

Subtract lower curve area from upper

$\int_a^b [f(x) - g(x)] \, dx$

Split into intervals & switch order

$\frac{4}{3}$

$\frac{14}{3}$

$g(x) = x$ is above

$\frac{1}{2}$

$x = \frac{\pi}{4}$ and $x = \frac{5\pi}{4}$

Find where curves intersect

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The Area of a Region Between Two Curves (VCE SSCE Mathematical Methods): Quizzes

Practise the questions

What is the key idea for finding area between two curves?

If f(x)≥g(x)f(x) \geq g(x)f(x)≥g(x) on [a,b][a,b][a,b], which formula gives the area?

What must you do when curves cross within the interval?

To find where y=x2y = x^2y=x2 and y=2xy = 2xy=2x intersect, solve:

What is the area between y=x2y = x^2y=x2 and y=2xy = 2xy=2x from x=0x = 0x=0 to x=2x = 2x=2?

Area of y=4−x2y = 4 - x^2y=4−x2 and y=x2+1y = x^2 + 1y=x2+1 from x=−1x = -1x=−1 to x=1x = 1x=1 is:

For f(x)=x3f(x) = x^3f(x)=x3 and g(x)=xg(x) = xg(x)=x, between x=0x = 0x=0 and x=1x = 1x=1, which is on top?

Total area between f(x)=x3f(x) = x^3f(x)=x3 and g(x)=xg(x) = xg(x)=x from x=−1x = -1x=−1 to x=1x = 1x=1 is:

Where do sin⁡x\sin xsinx and cos⁡x\cos xcosx intersect in [0,2π][0, 2\pi][0,2π]?

What is the crucial first step when finding area between curves?

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.

If $f(x) \geq g(x)$ on $[a,b]$ , which formula gives the area?

To find where $y = x^2$ and $y = 2x$ intersect, solve:

What is the area between $y = x^2$ and $y = 2x$ from $x = 0$ to $x = 2$ ?

Area of $y = 4 - x^2$ and $y = x^2 + 1$ from $x = -1$ to $x = 1$ is:

For $f(x) = x^3$ and $g(x) = x$ , between $x = 0$ and $x = 1$ , which is on top?

Total area between $f(x) = x^3$ and $g(x) = x$ from $x = -1$ to $x = 1$ is:

Where do $\sin x$ and $\cos x$ intersect in $[0, 2\pi]$ ?