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2 years ago

How to solve the indefinite integral

Mathematics

1 answer:

Minchanka [31]2 years ago

3 0

Answer:

$\frac{1}{4}x^4-x^2+3x+c$

Step-by-step explanation:

Use the the integration rules for powers of x: $\int x^n dx = \frac{1}{(n+1)} x^{n+1}$ and the additive property of integrals:

$f(x) = \int (x^3-2x+3)dx= \int x^3 dx-2\int x dx+\int 3 dx = \\=\frac{1}{4}x^4-x^2+3x+c$

with c being an arbitrary constant.

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Solve by the elimination method

Usimov [2.4K]

There is one solution. The solution of the system is (9,-5)

Option A is correct.

Step-by-step explanation:

We need to solve the system of equations by elimination method

$6x= 64+2y\\2x= -7-5y$

Rearranging the equations:

$6x-2y=64\,\,\,eq(1)\\2x+5y=-7\,\,\,eq(2)$

Eliminating y to find value of x:

Multiply eq(1) by 5 and eq(2) by 2 and add both equations:

$30x-10y=320\,\,\,\\4x+10y=-14\\--------\\34x=306\\x=\frac{306}{34}\\ x=9$

So, value of x= 9

Eliminating x to find value of y:

Multiply eq(1) by 2 and eq(2) by 6 and subtract both equations:

$12x-4y=128\\12x+30y=-42\\-\,\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\\---------\\-34y=170\\y=\frac{170}{-34}\\ y=-5$

So, value of y = -5

There is one solution. The solution of the system is (9,-5)

Option A is correct.

Keywords: Solving system of equations

Learn more about Solving system of equations at:

#learnwithBrainly

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3 years ago

The students in a class and the teacher visited a park on a field trip. The students were taught how to plant seeds, and the tea

drek231 [11]

The answer is B because the teacher is keeping count of the seeds that EACH student plants

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2 years ago

Read 2 more answers

The Midtown Bakery sells Chinese specialities such as pineapple buns and lotus seed buns. Day-old goods at the bakery are sold a

gayaneshka [121]

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3 years ago

Divide using synthetic division. ( x^4-12x^2-9)/(x+3)

Firdavs [7]

Answer:

x^3 - 3x^2 - 3x + 9 + (-36/(x+3))

x^3 - 3x^2 - 3x + 9 - (36/(x+3))

Step-by-step explanation:

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

x^4 + 0x^3 - 12x^2 + 0x -9

Coefficents: 1. 0. -12. 0 -9.

Please see the image for the next steps.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)

-36/(x+3)

6 0

2 years ago

What is the sum of the first 37 terms of the arithmetic sequence?

lidiya [134]

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

The sum of the first n terms of an arithmetic sequence is given by:

$S_{n} = \frac{n(a_{1} + a_{n})}{2}$

In this question:

$a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6$

We want the sum of the first 37 terms, so we have to find $a_{37}$

$a_{n} = a_{1} + (n-1)*d$

$a_{37} = a_{1} + (36)*d$

$a_{37} = -27 + 36*6$

$a_{37} = 189$

Then

$S_{37} = \frac{37(-27 + 189)}{2} = 2997$

The sum of the first 37 terms of the arithmetic sequence is 2997.

6 0

2 years ago