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Monica [59]
3 years ago
11

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating

rectangle. y = 3/x, y = 3/x2, x = 7 Find the area of the region

Mathematics
1 answer:
MakcuM [25]3 years ago
6 0

Answer:

A=8.4063u^{2}

Step-by-step explanation:

Be the functions:

y=\frac{3}{x};y=\frac{3}{x^{2}}:x=7

according the graph:

\int\limits^1_7 {\frac{3}{x} } \, dx -\int\limits^1_7 {\frac{3}{x^{2} } } \, dx =3\int\limits^1_7 {\frac{1}{x} } \, dx -3\int\limits^1_7 {\frac{1}{x^{2} } } \, dx=3(\int\limits^1_7 {\frac{1}{x} } \, dx -\int\limits^1_7 {\frac{1}{x^{2} } } \, dx)=3[lnx-\frac{1}{x}](1-7)=3[(ln7-ln1)-(\frac{1}{7}-1)]=3[(1.945-0)-(0.1428-1)]=3*(1.945+0.8571)=3*2.8021=8.4063u^{2}

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