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Using Accumulation Functions and Definite Integrals

AP Calculus AB· difficulty 3/5

t f'

By the net change theorem, ∫abf′(t) dt\int_a^b f'(t)\,dt equals:

  • A

    f(b)+f(a)f(b) + f(a)

  • B

    f(b)−f(a)f(b) - f(a)

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  • C

    f(b)+f(a)2\dfrac{f(b)+f(a)}{2}

  • D

    f′(b)−f′(a)f'(b) - f'(a)

Explanation

Net change theorem: ∫abf′(t) dt=f(b)−f(a)\int_a^b f'(t)\,dt = f(b) - f(a).

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