Calculuus

[cyan loom]

Group 2: Calculation of Areas between Curves

Calculate the area bounded by the curves
𝑦

sin
⁡
(
𝑥
)
y=sin(x) and
𝑦

sin
⁡
(
2
𝑥
)
y=sin(2x) in the interval
[
0
,
𝜋
]
[0,π].

Determine the area of the region enclosed by
𝑦

1
𝑥
y=
x
1
​
,
𝑦

𝑥
y=x, and
𝑦

1
4
𝑥
y=
4
1
​
x in the first quadrant.

Find the area between
𝑦

𝑥
4
−
2
𝑥
2
y=x
4
−2x
2
and
𝑦

2
𝑥
2
y=2x
2
.

Calculate the area of the region bounded by
𝑦

ln
⁡
(
𝑥
)
y=ln(x),
𝑦

0
y=0, and
𝑥

𝑒
2
x=e
2
.

Determine the area of the common region of the curves
𝑟

2
sin
⁡
(
𝜃
)
r=2sin(θ) and
𝑟

2
cos
⁡
(
𝜃
)
r=2cos(θ).

Let me know if you want any of these solved or graphed.

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[harsh island]

Could you actually just format it so that it’s readable?

Ok first question is the area bounded by the curves y=sin(x) and y=sin(2x) in [0,π]

I’m not going to take the effort to read the rest, please make your questions readable

[lusty lantern]

Let me know if you want any of these solved or graphed.
This thread is meant for you to get help, not for you to help us.

[cyan loom]

.

[lusty lantern]

Do you need help?

[harsh island]

I got this

I think

Ok @cyan loom do you have any idea how to start?

[cyan loom]

yh

[lusty lantern]

Start by graphing the curves with a rough sketch, and then determining which function is on top vs. bottom

[cyan loom]

applying trigonometric rules I suppose

and graphing

[cyan loom]

k

[harsh island]

Well a rough sketch works ig

You could also notice that both functions have the same starting point but sin(2x) grows faster at the start, so until some R ∈ [0,π], sin(2x) > sin(x)

Then you can find that R

[cyan loom]

ok

[fast musk]

@cyan loom

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