Quiz about Application Of Integrals

Question 1

What is the average value of $$\sqrt{x}$$ on the interval $$[5,12]$$ ?

Accepted Answer

Covalent bond

Answer

$$\frac{2}{21}[\sqrt{12^{3}}-\sqrt{5^{3}}]$$

Answer

$$\frac{1}{2}(\sqrt{12}-\sqrt{5})$$

Answer

$$\frac{2}{21}(\sqrt{12^{2}}-\sqrt{5^{2}})$$

Answer

$$\frac{1}{2}(\sqrt{12}+\sqrt{5})$$

Question 2

What is the average value of $$\frac{1}{x}$$ on the interval $$4 \leq x \leq 8$$ ?

Accepted Answer

Covalent bond

Answer

$$\frac{1}{4}\ln 2$$

Answer

$$\frac{\ln (32)}{4}$$

Answer

$$\frac{1}{16}$$

Answer

$$\frac{3}{16}$$

Question 3

What is the area of the region between the graphs of $$f(x)=3 e^{x}$$ and $$g(x)=-2$$ from $$x=0$$ to $$x=3$$ ?

Accepted Answer

Covalent bond

Answer

$$3(e^3+1)$$

Answer

$$3(e^3-1)$$

Answer

$$3 e^3$$

Answer

$$-3 e^3$$

Question 4

Consider the following problem:

The number of people in Bernardo's social network is increasing at a rate of $$r(t)=-2(t-3)^{2}+23$$ people per month (where $$t$$ is the time in months since Bernardo set up the network). At time $$t=4$$ months, Bernardo had 80 people in his social network. How many people were in Bernardo's social network at the end of the $$6^{	ext {th }}$$ month?

Accepted Answer

Covalent bond

Answer

$$80+\int_4^6 r(t) d t$$

Answer

$$\int_0^6 r(t) d t$$

Answer

$$\int_4^6 r(t) d t$$

Answer

$$r(6)$$

Question 5

What is the area of the region between the graphs of $${f}({x})=-x^{2}+2 x+12$$ and $$g({x})=x^{2}-12$$ from $${x}=-3$$ to $$x=4$$ ?

![](http://admin.getprephub.com/media/editor/aoi32_20221027213429997005.png)

Accepted Answer

Covalent bond

Answer

$$\frac{343}{3}$$

Answer

$$\frac{255}{4}$$

Answer

$$\frac{33}{31}$$

Answer

$$\frac{34}{13}$$

Application Of Integrals Calculus Maths Problems and Solutions

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