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Punchy
Punchy asked in Science & MathematicsMathematics · 1 year ago

Suppose that the integral from -2 to 5 of g(x)dx = 5. What is the integral from -4 to 3 of g(x+2)dx?

3 Answers

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  • ?
    Lv 7
    1 year ago

    Note that from highschool functions,  g(x+2) from -4 to 3, has the same "shape" of

    g(x) from -2 to 5.  [ Recall that g(x-a) is a horizontal shift of "a" units].

    So integral g(x)  from x=-2 to 5 is the same as

    integral of g(x+2) from -4 to 3.

    Now, to make this 'nicer',just formalize formalize this with a substitution in your g(x+2) integral.

  • alex
    Lv 7
    1 year ago

    let u = x+2

    --->the integral from -4 to 3 of g(x+2)dx = the integral from -2 to 5 of g(u)du = .....

  • RealPro
    Lv 7
    1 year ago

    Your hint is clearly that g(x+2) is just g(x) translated 2 units to the left.

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