A) \[\frac{104}{15}\pi \]cu unit
B) \[\frac{42\pi }{15}\]cu unit
C) \[\frac{52\pi }{15}\]cu unit
D) None of these
Correct Answer: A
Solution :
The given equation of curves are \[y={{x}^{2}}+1\] ...(i) and \[y=2x+1\] ...(ii) On solving Eqs. (i) and (ii), we get \[x=0,2\] \[\therefore \]Required volume \[=\pi \int_{0}^{2}{[{{(2x+1)}^{2}}-{{({{x}^{2}}+1)}^{2}}]}\,dx\] \[=\pi \int_{0}^{2}{(-{{x}^{4}}+2{{x}^{2}}+4x)}\,dx\] \[=\pi \left[ -\frac{{{x}^{5}}}{5}+\frac{2{{x}^{3}}}{3}+\frac{4{{x}^{2}}}{2} \right]_{0}^{2}\] \[=\frac{104\pi }{15}\pi \,cu\text{ }unit\]
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