Question

Find the exact coordinates of the centroid.

Answer 1

y = 4x, y = 0, x = 1

Answer 2

\[A = \frac{ 1 }{ 2 }bh = 1\]\[x = \frac{ 1 }{ A }\int\limits_{a}^{b}xf(x)dx = \int\limits_{0}^{1}x(4x)dx = \frac{ 4 }{ 3 }x^3]_{0}^{1}= 4/3\]\[y = \frac{ 1 }{ A }\int\limits_{a}^{b}0.5[f(x)^2]dx=\int\limits_{0}^{1}(0.5)(4x)^2dx = \int\limits_{0}^{1}\frac{ 16x^2 }{ 2 }dx=\frac{ 8 }{ 3 }x^3]_{0}^{1}=8/3\]

Messed up somewhere.

Answer 3

how did you get area = 1 ?

Answer 4

Oh, I derped on that part, so the area is 2?

Answer 5

If I plug in x = 1, the base will be 1 and height 4 -- 4/2 = 2?

Answer 6

yes

Answer 7

Thanks for the rescue @phi, got the answer now. Minor setbacks hehe