The Fundamental Theorem of Calculus (HSC SSCE Mathematics Advanced): Quizzes

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The Fundamental Theorem of Calculus
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What defines F(x)F(x) as a primitive of f(x)f(x)?

F(x)=f(x)F'(x) = f(x)

What is the primitive of x5x^5?

x66+C\frac{x^6}{6} + C

Why doesn't the power rule work when n=1n = -1?

It requires dividing by zero

The fundamental theorem states abf(x)dx\int_a^b f(x) dx equals what?

F(b)F(a)F(b) - F(a)

To integrate x(x+3)x(x+3), what must you do first?

Expand to x2+3xx^2 + 3x

To integrate x53x2x2\frac{x^5 - 3x^2}{x^2}, what should you do?

Split into x33x^3 - 3

What is 12x3dx\int_1^2 x^{-3} dx equal to?

38\frac{3}{8}

Why can't you integrate x4x^{-4} from 1-1 to 11?

Function undefined at x=0x=0 (asymptote)

To evaluate 253x2dx\int_2^5 3x^2 dx, what is the first step?

Find primitive: x3x^3

When substituting limits into [x32x]14[x^3 - 2x]_1^4, why use brackets?

Multiple terms prevent calculation errors

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