The Fundamental Theorem of Calculus and the Definite Integral (VCE SSCE Mathematical Methods): Quizzes

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The Fundamental Theorem of Calculus and the Definite Integral
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Why does the constant cc appear in indefinite integrals like f(x)dx=F(x)+c\int f(x) dx = F(x) + c?

Differentiation of a constant equals zero

What is the signed area for regions below the xx-axis?

Negative signed area

The Fundamental Theorem of Calculus states abf(x)dx\int_a^b f(x) dx equals what?

G(b)G(a)G(b) - G(a) where GG is antiderivative

What happens to the arbitrary constant cc when evaluating definite integrals?

It cancels out

If 23x2dx=193\int_2^3 x^2 dx = \frac{19}{3}, what is 32x2dx\int_3^2 x^2 dx?

193-\frac{19}{3}

What does aaf(x)dx\int_a^a f(x) dx equal?

00

The notation [G(x)]ab[G(x)]_a^b means evaluate G(x)G(x) at upper limit bb then do what?

Subtract value at lower limit aa

The additive property states abf(x)dx=acf(x)dx\int_a^b f(x) dx = \int_a^c f(x) dx plus what?

cbf(x)dx\int_c^b f(x) dx

For areas A1A_1 above and A2A_2 below the xx-axis, what is the signed area?

A1A2A_1 - A_2

What does abkf(x)dx\int_a^b k f(x) dx equal using the constant multiple property?

kabf(x)dxk \int_a^b f(x) dx

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