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Lady bird [3.3K]
3 years ago
7

Integral (x pangkat 3 - cos x) dx

Mathematics
1 answer:
ch4aika [34]3 years ago
6 0

You can break the integral of a sum/difference into the sum/difference of the integrals:


\int (x^3-\cos(x))\;dx = \int x^3\; dx - \int \cos(x)\; dx


The first integral can be solved using the power rule for integrations:


\int x^n\; dx = \frac{x^{n+1}}{n+1} \implies \int x^3\; dx = \frac{x^4}{4}


As for the second, remember the chain of derivation of trigonometric functions:


\sin(x) \to \cos(x) \to -\sin(x) \to -\cos(x) \to \sin(x) \ldots


The integration chain is the same, but it follows the opposite direction: the integral of the cosine function is the sine function. So, you have


- \int \cos(x)\; dx = -\sin(x)


Since this is an indefinite integral, we must add the generic costant to the answer:


\frac{x^4}{4} -\sin(x) + C

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Marina CMI [18]
Check the picture below.

now, the sides at the bottom, the straight sides, are plain to see how long each is, you can pretty much count the units off the grid.

so, the only ones you need the distance formula or pythagorean theorem is the slanted ones, there are two, and both are equal, so, just get the length of one, and double it up.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
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%  (c,d)
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\\\\\\
d=\sqrt{(6-2)^2+(4-7)^2}\implies d=\sqrt{4^2+(-3)^2}\implies d=\sqrt{16+9}
\\\\\\
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double that up, and both slanted sides are 10, the perimeter is all sides summed up.

5 0
3 years ago
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Step-by-step explanation:

please mark brainleist

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ioda
Needs more information
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