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calculus (please with steps and explanations)

consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral:
(a) definite integral from 0(on the bottom of the integral sign) to 5(top of integral sign) of[f(x)+2]dx

(b) definite integral from -5(bottom of integral sign) to 5(top of integral sign) f(x)dx, given that f is an even function.

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Linda

  1. This was done by Damon, but here's my take

    ∫[0,5](f(x)+2) dx
    = ∫[0,5] f(x) dx + ∫[0,5] 2 dx
    = 4 + 2x[0,5]
    = 4 + 10
    = 14

    Since we are dealing with an even function,
    ∫[-5,5] f(x) dx = 2∫[0,5] f(x) dx = 2*4 = 8

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    Steve

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