Volume With Known Cross Sections

Question

Let R be the region enclosed by the graphs of $$y = \sqrt{x}$$ and $$y = x^2$$. Region R is the base of a solid. For this solid, each cross section perpendicular to the *y*-axis is an isosceles right triangle with the length of each leg equal to the width of R at that *y*-value. Which of the following integrals gives the volume of the solid?

Accepted Answer

$$ \frac{1}{2} \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$

Answer

$$ \frac{1}{4} \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$

Answer

$$ \frac{1}{2} \int_0^1 (\sqrt{x} - x^2)^2 \, dx $$

Answer

$$ \int_0^1 (\sqrt{y} - y^2)^2 \, dy $$

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	dltkddnjs0925	2	2	0m 00s	200
#2	whizkri	1	1	0m 50s	50
#3	iainhsu647	1	1	1m 24s	16
#4	haneesh19.12	1	1	1m 28s	12
#5	manyab1708	1	1	1m 47s	-7
#6	sophieyao08	1	2	1m 43s	-13
#7	johnhhajjar0	1	1	1m 53s	-13
#8	bryantche0218	1	1	5m 15s	-215
#9	srinikasriyamathur	1	2	2h 06m	-7,495

Volume With Known Cross Sections

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