Engineering Board Exam Reviewer · Definite Integrals · easy

Find the average value of f(x)=xsqrt(x2+9) on the interval [0,4].

1. 98/3
2. 49/12
3. 49/3
4. 49/6

Answer

D. 49/6

Solution

favg=1/4-0 04xsqrt(x2+9),dx. With u=x2+9: 04xsqrt(x2+9),dx= 13≤ft[(x2+9)3/2 ]04=125-27/3=98/3. So favg= 14·98/3=49/6.

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