Question

plz help me with these 3 quextions!!!
10.The base of a solid is the first-quadrant area bounded by the line 4x + 5y = 20 and the coordinate axes. Write the definite integral to find the volume of the solid if every plane section perpendicular to the x-axis is a square. Do not evaluate.
15. Write the definite integral to find the smaller area cut from the circle x2 + y2 = 25 by the line x = 3. Do not integrate
18. The region bounded by y = tan(x), y = 0, x = pi/4 is rotated about the x-axis. The volume generated equals

Answer 1

Type 1 question at a time so it someone can help you answer it thoroughly :)

Answer 2

so the answer to question 10 involves a knowledge of calculus and geometry. the graph kind of looks like this. now we know that the plane seciton perpendicular to the axis is a square. so to get the integral, we would have to multiple the function by itself and then multiple by the width (dx), or \[\int\limits_{0}^{5} (f(x))^2dx\].

putting your equations in, you would get \[\int\limits_{0}^{5}(4-(\frac{ 4 }{ 5 }x))^2dx\].

lets see if you can do the rest on your own.

Answer 3

You forgot to multiply by pi since you're finding the volume by rotating it about the x-axis that creates a disk shape

Answer 4

@guardianoflore

Answer 5

but the thing is you're not rotating it about the x-axis. the plane section is a "square". using geometry, you realize the the function (f(x)) is simply squared to get the planar section. there's no rotation in the problem at all.