How can i add the fractions using a giant one to create a conmon 1 denominator /4+5/8

1 answer:

8 0

Stack them on top of each other and find the common denominator then multiply to total the denominator. Ex. 1/4 denominator is 8. 4x2 is 8. So 1 times what equals 8. 1! Then you should a new fraction 8/8 which is equivalent to 1.

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$\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx$

Each cylindrical shell has radius $2-x$ (the horizontal distance from the axis of revolution to the curve $y=8x^3$ ); has height $8x^3$ (the vertical distance between a point on the $x$ -axis in $0\le x\le1$ and the curve $y=8x^3$ ).

Compute the integral.

$\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}$