You need to determine the length of the vector function `bar r(t) =` `ltcos^3 t, sin^3 t, 2gt, ` over interval `[0,pi/2], ` hence you need to find the magnitude of the tangent vector such that:

`|bar r'(t)| = sqrt((3cos^2 t*(-sin t))^2 + (3sin^2 t*cos t)^2)`

`|bar r'(t)| = sqrt(9cos^4 t*sin^2 t + 9sin^4 t*cos^2 t) `

`|bar r'(t)| =...

(The entire section contains 193 words.)

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