Volume of resulting solid which is enclosed by curve y = x and y = x2 is rotated about x-axis

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Suresh Chand · Accepted Answer

After Rotating to about x-axis The total volume of solid is (V = int dv = pi int_a^b (r_0^2 - r_1^2) dx) Then in this case, we have r0 = x r1 = x2 a = 0 b = 1 Now, (V = int dv = pi int_a^b (r_0^2 - r_1^2) dx) (= pi int_0^1 [x^2 - (x^2)^2] dx) (= pi int_0^1 [x^2 - x^4] dx) (= pi left [ frac{x^{2+1}}{2+1} - frac{x^{4+1}}{4+1} right ]_0^1) (= pi left [ frac{x^3}{3} - frac{x^5}{5} right ]_0^1) (= pi left [ frac{5x^3 - 3x^5}{15} right ]_0^1) (= frac{pi}{15} left { [5(1)^3 - 3(1)^5] - [5(0)^3 - 3(0)^5] right }) (= frac{pi}{15} (5.1 - 3.1)) (= frac{2pi}{15})

Find the volume of the resulting solid which is enclosed by the curve y = x and y = x²is rotated about the x-axis.

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Find the volume of the resulting solid which is enclosed by the curve y = x and y = x2 is rotated about the x-axis.

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Find the volume of the resulting solid which is enclosed by the curve y = x and y = x²is rotated about the x-axis.