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JulsSmile [24]
3 years ago
13

A library shelf is 9 feet wide.a set of nature books fill 1/6 of the shelf space. each book in the set is 3/5 inch thick.how man

y books are in a set
Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0
Area filled by nature books = 1/6 of 9 feet = 1/6 x 9 = 3/2 feet.

Number of nature books = 3/2 / 3/5 = 2.5 ≈ 3 books.
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Answer:

\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c

Step-by-step explanation:

Note that the integral of 5^x is not \frac{1}{6}x^6 + c

The solution is as follows:

Given

5^x

Required

Integrate

Represent the given expression using integral notation

\int\limits {5^x} \, dx

This question can't be solved directly;

We'll make use of exponential rules which states;

\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c

By comparing \int\limits {5^x} \, dx with \int\limits {a^x} \, dx;

we can substitute 5 for a;

Hence, the expression \int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c becomes

\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c

-------------------------------------------------------------------------------------

However, the integral of x^5 is \frac{1}{6}x^6 + c

This is shown below:

Given that x^5

Applying power rule;

Power rule states that

\int\limits{x^n}\ dx = \frac{x^{n+1}}{n+1} + c

In this case (x^5), n = 5;

So, \int\limits{x^n}\ dx= \frac{x^{n+1}}{n+1} + c

becomes

\int\limits{x^5}\ dx = \frac{x^{5+1}}{5+1} + c

\int\limits{x^5}\ dx = \frac{x^{6}}{6} + c

\int\limits{x^5}\ dx= \frac{x^{6}}{6} + c

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