Question

### Gauthmathier9245

Grade 8 · 2021-02-01

Given f\left(x\right)=\sqrt {x-1}, verify the hypotheses of the Mean Value Theorem for Integrals f on [1,10] and find the value of c as indicated in the theorem.

Good Question (78)

Answer

4.7(771) votes

### Gauthmathier9603

Grade 8 · 2021-02-01

Answer

c=5

Explanation

The function f is continuous for x\geq 1, thus:

\int _{1}^{10}\sqrt {x-1}\d x=f\left(c\right)(10-1)\left. \dfrac {2(x-1)^{\frac{1}{2}}}{3}\right\rbrack^{10}_{1}=9f\left(c\right)

\dfrac {2}{3}\left[(10-1)^{\frac{1}{2}}-0\right]=9f\left(c\right)

18=9f\left(c\right);

2=f\left(c\right);

2=\sqrt {c-1};

4=c-1

5=c.

\int _{1}^{10}\sqrt {x-1}\d x=f\left(c\right)(10-1)\left. \dfrac {2(x-1)^{\frac{1}{2}}}{3}\right\rbrack^{10}_{1}=9f\left(c\right)

\dfrac {2}{3}\left[(10-1)^{\frac{1}{2}}-0\right]=9f\left(c\right)

18=9f\left(c\right);

2=f\left(c\right);

2=\sqrt {c-1};

4=c-1

5=c.

Thanks (52)

Does the answer help you? Rate for it!

## Still Have Questions?

Find more answers or ask new questions now.