Mean value theorem for integrals Quiz 1

Question 1

Apply Mean Value Theorem for integral to find for which value of c, where the function $$f\left( x \right) = \left( {3 + {x^2}} \right)$$ have average values across the integral $$\left( { - 1,2} \right).$$

Accepted Answer

$$1$$

Answer

$$0$$

Answer

$$ - 1$$

Answer

$$2$$

Question 2

Find value of c guaranteed by Mean Value Theorem for function $$f\left( x \right) = \sin 2x$$over $$\left( {0,\pi } \right).$$

Accepted Answer

$$0$$

Answer

$$\dfrac{{3\pi }}{2}$$

Answer

$$\dfrac{\pi }{2}$$

Answer

$$\dfrac{\pi }{4}$$

Question 3

Find the value of c for the function $$f\left( x \right) = \left( {x - 2} \right)$$ over $$\left( {0,4} \right).$$

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$1$$

Answer

$$3$$

Question 4

Find value of $$c$$ by Mean Value Theorem to the following function $$f\left( x \right) = {x^2}$$ over $$\left( {1,2} \right).$$

Accepted Answer

$$\left( {\sqrt {\dfrac{7}{3}} } \right)$$

Answer

$$\left( {\dfrac{{\sqrt 7 }}{3}} \right)$$

Answer

$$\left( {\dfrac{7}{{\sqrt 3 }}} \right)$$

Answer

$$\left( {\dfrac{7}{3}} \right)$$

Question 5

Apply Mean Value Theorem in the function and find the value of c where $$f\left( x \right) = {x^3}$$ over the interval $$\left( {0,3} \right).$$

Accepted Answer

$$1.88$$

Answer

$$1.02$$

Answer

$$1.42$$

Answer

$$2.09$$