The region in the first quadrant bounded by the x-axis, the line x = In(pi), and the curve y = sin(ex) is rotated about the x-axis. What is the volume of the generated solid? (5 points) 0.906
0.795
2.846
2.498​

D

Step-by-step explanation:

Please refer to the graph below.

So, we want to find the volume of the solid generated by revolving the green area about the x-axis.

We can use the disk method. The disk method is given by:

Where R(x) is the radius or height of the representative rectangle.

We are integrating from x = 0 to x = ln(π). The height of a representative rectangle is given by y. Therefore, the volume is:

Simplify:

Approximate. So, the volume of the generated solid is:

The solid is shown in the second figure.

(Courtesy of WolframAlpha.)

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116