Vertical and horizontal slicing Quiz 1

Question 1

Given that one of the curves is $${{x}^{2}}$$ and the other is $$-{{x}^{2}}+8$$. Calculate the value of the area such that the area is represented as a right Riemann sum of $$5$$ vertical slices.

Accepted Answer

$$20.48$$

Answer

$$-21.76$$

Answer

$$27.16$$

Answer

$$-21.76$$

Question 2

Two functions are given $$f(x)=2x+3$$ and $$f(x)={{x}^{2}}$$. John is trying to calculate the Riemann sum using vertical slices. Calculate the Left Riemann sum of the area formed by the two functions in the interval $$[2,3]$$.

Accepted Answer

$$1.96$$

Answer

$$\dfrac{3}{14\sqrt{14}}$$

Answer

$$\dfrac{1}{3}$$

Answer

$$14\sqrt{14}$$

Question 3

A researcher is trying to check whether using a particular slice makes a difference in calculating the area formed by $$\sin (2x)$$ and $$2\cos (x)$$. Calculate the area formed by the two functions using both a horizontal slice as well as vertical slice given the interval $$\left[ -\dfrac{\pi }{2},\dfrac{\pi }{2} \right]$$.

Accepted Answer

$$4$$

Answer

$$8-4\sin \left( \dfrac{\pi }{2} \right)$$

Answer

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

Answer

$$8-4	anh (2)$$

Question 4

A function $$f(x)=x{{e}^{x+5}}$$ is being rotated along the $$x-$$ axis. Given that the rotated sphere is being vertically sliced I n the interval $$[-3,3]$$, calculate the volume inside the interval.

Accepted Answer

$$\dfrac{1}{4}{{e}^{4}}(13{{e}^{2}}-25)\pi $$

Answer

$$\dfrac{1}{4}{{e}^{4}}(13{{e}^{2}}-16)\pi $$

Answer

$$\dfrac{1}{4}{{e}^{4}}(3{{e}^{2}}-25)\pi $$

Answer

$$\dfrac{1}{2}{{e}^{4}}(13{{e}^{2}}-25)\pi $$

Question 5

Given two functions $$-{{e}^{2x}}+5$$ and $${{e}^{x}}$$, calculate the area made by vertical slices in the interval $$\left[ 0,\dfrac{\ln (5)}{2} \right]$$

Accepted Answer

$$-0.395$$

Answer

$$0.395$$

Answer

$$14.47$$

Answer

No Solution