Answer to Question #154224 in Calculus for mafizur alam

Question #154224

find the surface area of the object obtained by rotating y=4+3x^2, 1<=x<=2


1
Expert's answer
2021-01-11T14:38:47-0500


Surface area obtained by rotating the curve about y axis

will be

S=122πx(1+(y1)2)dx\int_{1}^{2}2\pi x\sqrt{(1+(y_1)^2)}dx [ where the y1y_1 is the differentiation with respect to x]

    122πx(1+(6x)2)dx    π361272x(1+(6x)2)dx    π3636144(1+z)dz    π3623(1+z)3236144    π54[145323732]\implies\int_1^22\pi x\sqrt{(1+(6x)^2)}dx\\\implies\frac{\pi}{36}\int_1^272 x\sqrt{(1+(6x)^2)}dx\\\implies\frac{\pi}{36}\int_{36}^{144}\sqrt{(1+z)}dz\\\implies\frac{\pi}{36}\frac{2}{3}(1+z)^\frac{3}{2}|_{36}^{144}\\\implies\frac{\pi}{54}[145^\frac{3}{2}-37^\frac{3}{2}] [Here we take Z=36x2]

So area of the given curve is π54[145323732]\frac{\pi}{54}[145^\frac{3}{2}-37^\frac{3}{2}]


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment