3 years ago

Question 2(Multiple Choice Worth 5 points)

Mathematics

1 answer:

KengaRu [80]3 years ago

8 0

I believe the correct answer to this question is 42 and 288. If im not wrong.

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Which of these shapes have the same area?

zvonat [6]

Answer:

wheres the picture?

Step-by-step explanation:

3 0

3 years ago

∫∫x²(y-x)dxdy ,d là miền giới hạn bởi các đường y=x² và x=y²

Valentin [98]

It looks like the integral is

$\displaystyle \iint_D x^2 (y-x) \,\mathrm dx\,\mathrm dy$

where D is the set

D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}

So we have

$\displaystyle \iint_D x^2(y-x)\,\mathrm dx\,\mathrm dy = \int_0^1 \int_{x^2}^{\sqrt x} x^2(y-x)\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \left(\frac{x^2y^2}2-x^3y\right)\bigg|_{y=x^2}^{y=\sqrt x} \\\\ = \int_0^1 \left(\frac{x^3}2-x^{7/2}+x^5-\frac{x^6}2\right)\,\mathrm dx \\\\ = \left(\frac{x^4}8 - \frac{2x^{9/2}}9 + \frac{x^6}6 - \frac{x^7}{14}\right)\bigg|_{x=0}^{x=1} = \frac18-\frac29+\frac16-\frac1{14} = \boxed{-\frac{1}{504}}$