Leaving Cert Integration Set C Questions - L.C. Maths

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Algebra 1

0/14

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Start with the quiz…

Knowledge Check Quiz

EXAMS.IE

Integration & Areas

Hint

Integration uses infinitely narrow rectangles to calculate the area.

1 / 5

Integration is used to estimate the area under a curve.

True

False

Integration uses infinitely narrow rectangles to calculate the area exactly.

That's right!

Integration uses infinitely narrow rectangles to calculate the area exactly.

Hint

What is \(\int_3^2\,dx\)?

2 / 5

It is possible for an integral to be negative.

True

False

For example, \(\int_3^2\,dx\) is negative.

That's right!

For example, \(\int_3^2\,dx\) is negative.

Hint

We add up the areas of vertical rectangles.

3 / 5

Which of the following is the area between a curve and the \(x\) axis?

\(\int_a^b f(x)\,dx\)

\(\int_a^b f(y)\,dx\)

\(\int_a^b f(x)\,dy\)

\(\int_a^b f(y)\,dy\)

We add up the areas of vertical rectangles.

That's right!

We add up the areas of vertical rectangles.

Hint

We add up the areas of horizontal rectangles.

4 / 5

Which of the following is the area between a curve and the \(y\) axis?

\(\int_a^b f(x)\,dx\)

\(\int_a^b f(y)\,dx\)

\(\int_a^b f(x)\,dy\)

\(\int_a^b f(y)\,dy\)

We add up the areas of horizontal rectangles.

That's right!

We add up the areas of horizontal rectangles.

Hint

This is equivalent to removing the area between the \(x\) axis and the lower curve.

5 / 5

Which of the following is the area between two curves \(y=f(x)\) and \(y=g(x)\)?

\(\int_a^b (g(x)+f(x))\,dx\)

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

\(\int_a^b g(x)f(x)\,dx\)

\(\int_a^b \dfrac{g(x)}{f(x)}\,dx\)

This is equivalent to removing the area between the \(x\) axis and the lower curve.

That's right!

This is equivalent to removing the area between the \(x\) axis and the lower curve.

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