The Definite Integral and Its Properties (HSC SSCE Mathematics Advanced): Quizzes

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The Definite Integral and Its Properties
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How does a region below the xx-axis contribute to a definite integral?

It contributes a negative value

What is ∫−aaf(x)dx\int_{-a}^{a} f(x)dx if f(x)f(x) is an odd function?

00

What is ∫−aaf(x)dx\int_{-a}^{a} f(x)dx if f(x)f(x) is an even function?

2∫0af(x)dx2\int_{0}^{a} f(x)dx

Which property allows breaking an integral at point cc?

∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx\int_{a}^{b} f(x)dx = \int_{a}^{c} f(x)dx + \int_{c}^{b} f(x)dx

What is the value of ∫aaf(x)dx\int_{a}^{a} f(x)dx?

00

How does reversing integration limits affect the result?

∫abf(x)dx=−∫baf(x)dx\int_{a}^{b} f(x)dx = -\int_{b}^{a} f(x)dx

What does ∫ab(f(x)+g(x))dx\int_{a}^{b} (f(x) + g(x))dx equal?

∫abf(x)dx+∫abg(x)dx\int_{a}^{b} f(x)dx + \int_{a}^{b} g(x)dx

What does ∫abkf(x)dx\int_{a}^{b} kf(x)dx equal where kk is a constant?

k∫abf(x)dxk\int_{a}^{b} f(x)dx

If f(x)≤g(x)f(x) \leq g(x) on [a,b][a,b], what can we conclude about their integrals?

∫abf(x)dx≤∫abg(x)dx\int_{a}^{b} f(x)dx \leq \int_{a}^{b} g(x)dx

What is ∫−22(x3−4x)dx\int_{-2}^{2} (x^3 - 4x)dx?

00

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