Further Applications of Integration (HSC SSCE Mathematics Advanced): Quizzes

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Further Applications of Integration
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What is the primitive of 1x\frac{1}{x}?

log⁡e∣x∣+C\log_e|x| + C

What formula finds area between two curves from x=ax=a to x=bx=b?

∫ab(top−bottom)dx\int_a^b (\text{top} - \text{bottom}) dx

In the area formula, what do aa and bb represent?

xx-coordinates of intersection points

Why is sketching curves important when finding areas?

Identifies which curve is on top

For the hyperbola xy=2xy = 2, what are the asymptotes?

Both coordinate axes

What is the value of log⁡e1\log_e 1?

00

Between x=1x=1 and x=2x=2, which is above: line y=3−xy=3-x or hyperbola y=2xy=\frac{2}{x}?

The line y=3−xy = 3 - x

How can the hyperbola xy=2xy = 2 be rewritten?

y=2xy = \frac{2}{x}

What is ∫kxdx\int \frac{k}{x} dx using the constant multiple rule?

klog⁡e∣x∣+Ck\log_e|x| + C

What happens if you subtract curves in the wrong order?

You get a negative area

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