Cambridge Integration Question (1 Viewer)

Ambility · Nov 2, 2015

Question 14a from Cambridge 3 Unit Year 11 Exercise 11E

$Sketch $y=x^2$ and mark the points A(a, $a^2$), B(-a, $a^2$), P(a, 0) and Q(-a,0).$\\$Show that $\int^a_0 x^2 \, dx = \frac{2}{3}$ (area of triangle OAP).$

Drongoski · Nov 2, 2015

Don't have the latest text. Is it about the integral being equal to 2/3(area of triangle AOP)?

If so - it's very straightforward.

The integral = a³/3

Area of the triangle = 1/2 * a * a² = a³/2

Hence the required result.

Ambility · Nov 2, 2015

Drongoski said:
Don't have the latest text. Is it about the integral being equal to 2/3(area of triangle AOP)?

If so - it's very straightforward.

The integral = a³/3

Area of the triangle = 1/2 * a * a² = a³/2

Hence the required result.

Oh that makes sense, thanks.

Cambridge Integration Question (1 Viewer)

Ambility

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Drongoski

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Ambility

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