Question

Find the area of the region. Use a graphing utility to verify your result.
y = 7 sin(x) + sin(7x)

Answer 1

@ganeshie8 help?

Answer 2

i got 14.286, but its wrong:(

Answer 3

@jim_thompson5910

Answer 4

this is in the wrong section, but that's fine

\[\Large f ' (x) = 7\sin(x) + \sin(7x)\]

\[\Large f(x) = \int (7\sin(x) + \sin(7x))dx\]

\[\Large f(x) = \int (7\sin(x))dx + \int(\sin(7x))dx\]

\[\Large f(x) = 7\int (\sin(x))dx + \int(\sin(7x))dx\]

\[\Large f(x) = 7\int (\sin(x))dx + \frac{1}{7}\int(\sin(u))du \ ... \ u = 7x\]

\[\Large f(x) = 7(-\cos(x)) + \frac{1}{7}(-\cos(7x))+C\]

\[\Large f(x) = -7\cos(x) - \frac{1}{7}\cos(7x)+C\]

Answer 5

wait, what endpoints does it give you?

Answer 6

@jim_thompson5910 sorry i just saw it

Answer 7

look

Answer 8

which region are they referring to? what are the endpoints?

Answer 9

ok from 0 to pi

Answer 10

so you need to calculate f(pi) - f(0)

Answer 11

thats exactly what i did and i got 14.286

Answer 12

i also used wolfram to verify and it was the same answer

Answer 13

write it as a fraction

Answer 14

not the approximate answer

Answer 15

what do you get?

Answer 16

okay give me a second

Answer 17

wolfram isn't giving me anything now. let me correct it

Answer 18

do you see how I got

\[\Large f(x) = -7\cos(x) - \frac{1}{7}\cos(7x)+C\]

Answer 19

1/100

Answer 20

100/7

Answer 21

yes:)

Answer 22

is 100/7 my answer then?

Answer 23

correct

Answer 24

i see:) it was correct! thank you!

Answer 25

you're welcome