Last updated on Oct 23, 2026

Area Between Two Curves (Leaving Cert Mathematics): Quizzes

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Area Between Two Curves

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To find area between two curves, what do you subtract from the upper curve's area?

Lower curve's area with x-axis

What is $\int_0^1 x^2 dx$ equal to?

$\frac{1}{3}$

What is $\int_0^1 x^3 dx$ equal to?

$\frac{1}{4}$

What is the area between $y = x^2$ and $y = x^3$ from $x = 0$ to $x = 1$ ?

$\frac{1}{12}$

What is the alternative method for finding area between curves $f(x)$ and $g(x)$ ?

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

At what points do $y = x^2 + 1$ and $y = 11 - \frac{9}{x^2}$ intersect?

$(1, 2)$ and $(3, 10)$

Which is the upper curve between $y = x^2 + 1$ and $y = 11 - \frac{9}{x^2}$ from $x = 1$ to $3$ ?

$y = 11 - \frac{9}{x^2}$

How is $\frac{9}{x^2}$ written using negative exponents?

$9x^{-2}$

What is $\int_1^3 (11 - 9x^{-2}) dx$ equal to?

$16$

What is $\int_1^3 (x^2 + 1) dx$ equal to?

$\frac{32}{3}$

What is the area between $y = x^2 + 1$ and $y = 11 - \frac{9}{x^2}$ from $x = 1$ to $3$ ?

$\frac{16}{3}$

Simplifying $(11 - 9x^{-2}) - (x^2 + 1)$ gives which integrand?

$10 - 9x^{-2} - x^2$

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Average Value of a Function

Area Under/Between Curves

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