The average value of on the interval is

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The average value of f(x)=1+4xf(x)=\sqrt{1+4x} on the interval [1,5][1,5] is (a) 130(213/2−53/2)\displaystyle\frac{1}{30}\bigl(21^{3/2}-5^{3/2}\bigr) (b) 21+52\displaystyle\frac{\sqrt{21}+\sqrt{5}}{2} (c) 124(213/2−53/2)\displaystyle\frac{1}{24}\bigl(21^{3/2}-5^{3/2}\bigr) (d) 112(213/2−53/2)\displaystyle\frac{1}{12}\bigl(21^{3/2}-5^{3/2}\bigr)

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