Find the area under the curve y = 13/x3 from x = 1 to x = t. Evaluate the area under the curve for t = 10, t = 100, and t = 1000. t = 10 t =

Question

Find the area under the curve y = 13/x3 from x = 1 to x = t. Evaluate the area under the curve for t = 10, t = 100, and t = 1000. t = 10 t = 100 t = 1000 Find the total area under this curve for x ≥ 1.

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Nevaeh 3 weeks 2021-09-28T16:19:37+00:00 1 Answer 0

Answers ( )

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    2021-09-28T16:21:00+00:00

    Answer:

    t = 10

    A = 32496.75

    t = 100

    A = 324999996.8

    t = 1000

    A=3.25\times 10^{12}

    Step-by-step explanation:

    The area under the curve is calculated by using the following definite integral:

    A = \int\limits^t_ {1} \,{13\cdot x^{3}}  dx

    A = 13 \int\limits^t_1 {x^{3}} \, dx

    A = \frac{13}{4}\cdot (t^{4}-1)

    Evaluated areas are presented below:

    t = 10

    A = 32496.75

    t = 100

    A = 324999996.8

    t = 1000

    A=3.25\times 10^{12}

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