Question

Calculus Question!! Medal!!

Answer 1

You should plot the functions, and then find the areas of the figures.

Answer 2

plot the piecewise function. Because I did that

Answer 3

Exactly, then you see a rectangle and maybe a triangle

Answer 4

Here is the graph

Answer 5

Perfect, you have a trapezoid. Do you know the formula for the area of the trapezoid?

Answer 6

A = a+b / 2 h

Answer 7

Well, I don't know this expression. I usually use this,
\[A=(B+b)\cdot h/2\]

Answer 8

that is correct too I think

Answer 9

The graph you plot says, that B=6, b=2 and the height is 4, so you can calculate the area.

Answer 10

With B the bottom base, b the top base, and h the height.

Answer 11

how did you get B=6 and b=2?

Answer 12

You see that I say 6, because the integral tells you to do the area between 1 and 7

Answer 13

In the graph, the function cuts the x axis at 7, so you can see that the bottom base has the length of 6 units. For the top base the full length would be 3 (as the picewise function says), but the integral tells you the first value is x=1, so the top base has a length of 2.

Answer 14

okay so (6+2) *4 / 2

Answer 15

@John_ES

Answer 16

Yes, that the good answer.

Answer 17

16

Answer 18

is that correct?

Answer 19

Perfect.

Answer 20

Thanks for the help

Answer 21

You're welcome.