The Region Under the Curve $y=2 \sin ^{2} x$ $0 \leq x \leq \pi$

question 68

Multiple Choice

The region under the curve $y=2 \sin ^{2} x$ , $0 \leq x \leq \pi$ is rotated about the x-axis. Find the volume of the resulting solid.

• A) \(\frac{3}{4}\) \(\pi^{2}\)
• B) \(\frac{2}{\pi}\)
• C) \(\frac{6}{\pi^{2}}\)
• D) \(\frac{\pi}{6}\)
• E) \(\frac{\pi^{2}}{6}\)

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Definitions:

Arthritis

A group of painful, inflammatory conditions affecting joints and connective tissues, leading to stiffness and decreased range of motion.

Damage

Physical harm caused to something in such a way that it is impaired or its value is diminished.

Good

Describes something as being satisfactory, beneficial, or morally right.

Groin Pull

A strain or injury to the muscles of the inner thigh, often occurring in activities requiring sudden changes in direction or speed.