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.

Answer 1

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

$A=3.25\times 10^{12}$