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Area Between Curves

AP Calculus AB· difficulty 3/5

x a b f(x) g(x)

The shaded area between ff and gg from aa to bb equals:

  • A

    ∫ab(g(x)−f(x)) dx\int_a^b (g(x)-f(x))\,dx

  • B

    f(b)−g(a)f(b)-g(a)

  • C

    ∫abf(x)g(x) dx\int_a^b f(x)g(x)\,dx

  • D

    ∫ab(f(x)−g(x)) dx\int_a^b (f(x)-g(x))\,dx

    check_circle

Explanation

Since f≥gf \geq g on [a,b][a,b], the area equals ∫ab(f(x)−g(x)) dx\int_a^b (f(x) - g(x))\,dx.

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