Last updated on Sep 21, 2026

Area Under/Between Curves (Leaving Cert Mathematics): Quizzes

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Area Under Curve and x-axis

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What represents the area under $y = f(x)$ from $a$ to $b$ ?

A definite integral

If $f(x) \geq 0$ on $[a,b]$ , the integral gives:

Total area above x-axis

If $f(x) \leq 0$ on $[a,b]$ , the definite integral is:

Negative value (below axis)

If $f(x)$ changes sign on $[a,b]$ , the integral gives:

Net area (pos minus neg)

Main steps to compute area under curve?

Find antiderivative then $F(b)-F(a)$

Value of $\int_0^2 x^2 dx$ is:

$\frac{8}{3}$

Value of $\int_0^\pi \sin x \, dx$ equals:

2

If curve lies below $x$ -axis, actual area is:

Absolute value of integral

Area between $y=f(x)$ and $y=g(x)$ with $f\geq g$ is:

$\int(f-g) dx$

Area between $x^2$ and $x+2$ from $0$ to $1$ is:

$\frac{13}{6}$

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Average Value of a Function

Area Under/Between Curves

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The Basics

Average Value of a Function

Area Under/Between Curves

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The Basics

Average Value of a Function

Area Under/Between Curves

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The Basics

Average Value of a Function

Area Under/Between Curves

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