Interactive multiple-choice quiz: اختبار في تطبيقات التكامل: حساب الحجوم الدورانية

A

\(v = \pi \int_0^4 (\sqrt{y})^2 dy\)

B

\(v = \pi \int_{-2}^2 (4 - x^2)^2 dx\)

C

\(v = \pi \int_0^4 [(2 + \sqrt{y})^2 - (2 - \sqrt{y})^2] dy\)

D

\(v = \pi \int_0^4 [(4 + \sqrt{y})^2 - (4 - \sqrt{y})^2] dy\)

A

\(v = \pi \int_0^2 (4 - x^2)^2 dx\)

B

\(v = \pi \int_0^4 (\sqrt{y})^2 dy\)

C

\(v = \pi \int_0^4 [(2 + \sqrt{y})^2 - (2 - \sqrt{y})^2] dy\)

D

\(v = \pi \int_0^4 [(4 + \sqrt{y})^2 - (4 - \sqrt{y})^2] dy\)

A

\(v = \pi \int_0^4 (\sqrt{y})^2 dy\)

B

\(v = \pi \int_{-2}^2 [(6 - x^2)^2 - 2^2] dx\)

C

\(v = \pi \int_0^4 [(6 + \sqrt{y})^2 - (6 - \sqrt{y})^2] dy\)

D

\(v = \pi \int_0^4 [(4 + \sqrt{y})^2 - (4 - \sqrt{y})^2] dy\)

A

\(\frac{\pi}{6}\)

B

\(\frac{\pi}{5}\)

C

\(\frac{\pi}{2}\)

D

\(\frac{32\pi}{5}\)

A

\(v = \int_0^2 \pi (3)^2 dx + \int_0^2 \pi (2 - x)^2 dx\)

B

\(v = \int_0^2 \pi (3 - (2 - x))^2 dx\)

C

\(v = \pi \int_0^2 (3)^2 dx - \pi \int_0^2 (3 - (2 - x))^2 dx\)

D

\(v = \int_0^2 \pi (3) dx + \int_0^2 \pi (3 - (2 - x))^2 dx\)

A

\(v = \pi \int_0^1 ((3 - y)^2 - [3 - (2 - y)]^2) dy\)

B

\(v = 2\pi \int_0^1 ((3 - y)^2 - [3 - (2 - y)]^2) dy\)

C

\(v = \pi \int_0^1 ((3 - y)^2 - (2 - y)^2) dy\)

D

\(v = \pi \int_0^1 ((3 - y)^2 - [3 + (2 - y)]^2) dy\)

A

\(16\pi\)

B

\(\frac{128\pi}{3}\)

C

\(\frac{256\pi}{3}\)

D

\(256\pi\)

A

\(v = \int_2^9 \pi (9 - y)^2 dy\)

B

\(v = \int_2^9 \pi \sqrt{9 - y} dy\)

C

v = \int₂⁹ (9 - y)² dy

D

\(v = \int_2^9 \pi (9 - y) dy\)