2 years ago

Graph the system below and write its solution. 1 Y=3x+1 - 2x+y=6

Mathematics

1 answer:

klemol [59]2 years ago

5 0

Y=3x+1

-2x+y=6

I recommend using this other app as well it’s as good as Brainly

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The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th

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Answer:

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Step-by-step explanation:

To find:

∫ $6x^5(x^6-2)\,dx$

Solution:

Method of substitution:

Let $x^6-2=t$

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[use $(x^n)'=nx^{n-1}$ ]

So,

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(Use ∫ $t^n\,dt=\frac{t^{n+1} }{n+1}$ )

Put $t=x^6-2$

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So,

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C$

where $C=2+C_1$

Without using substitution:

∫ $6x^5(x^6-2)\,dx$ = ∫ $6x^{11}-12x^5\,dx$ = $\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C$

So, same answer is obtained in both the cases.

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