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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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4. What is the solution of the system of equations?<br> y=-2x+5<br> y=-2x+20

Norma-Jean [14]

The system of equation, y = -2x + 5 and y = -2x + 20, have no solution.

<h3>How to Find the Solution of a System of Equations?</h3>

The solution to a system of equations is the ordered pair of x and y that makes both equations true.

Given the system of equations,

y = -2x + 5 --> equation 1

y = -2x + 20 --> equation 2

Subtract to eliminate variable "y"

0 = 0 + 25

0 = 25 [this is not true]

Therefore, no solution exist for the system of equations.

Thus, we can conclude that, the system of equation, y = -2x + 5 and y = -2x + 20, have no solution.

Learn more about system of equations on:

brainly.com/question/14323743

#SPJ1

3 0

1 year ago

If f(x) = x2 - 1 and g(x) = 2x - 3, what is the domain of (fog)(x)?

ladessa [460]

Answer:

domain will be ( -∞, ∞)

Step-by-step explanation:

The given functions are f(x) = x² - 1 and g(x) = 2x - 3

We have to find domain of (fog)(x)

We will find the function (fg)(x) first.

(fog)(x) = f[g(x)]

= (2x - 3)²

= 4x² + 9 - 12x - 1

= 4x² - 12x + 8

= 4 (x² - 3x + 2)

The given function is defined for all values of x.

Therefore, domain will be ( -∞, ∞)

<u>brainly.com/question/2458431</u>

4 0

2 years ago

Which of the following functions have a vertical asymptote for values of Ø such that cos Ø = 1?Select all that apply.

igomit [66]

Answer:

$y=\cot \theta$ and $y=\csc \theta$

Step-by-step explanation:

Note that if $\cos \theta=1,$ then $\sin \theta=0.$

Functions $y=\cos \theta,\ \ y=\sin \theta$ do not have vertical asymptotes at all.

Vertical asymptotes have functions $y=\tan \theta,\ \ y=\cot \theta,\ \ y=\sec \theta,\ \ y=\csc \theta.$

Functions $y=\tan \theta$ and $y=\sec \theta$ have the same vertical asymptotes (when $\cos \theta =0$ ).

Functions $y=\cot \theta$ and $y=\csc \theta$ have the same vertical asymptotes (when $\sin \theta =0$ ). See attached diagram

3 0

3 years ago

Graph the line for y+1=−3/5(x−4) on the coordinate plane. Move Line Undo Redo Reset

dsp73

Answer:

The equation of line is shown below.

Step-by-step explanation:

The equation of line is

$y+1=\frac{-3}{5}(x-4)$

It is the point slope form of a line, therefore the slope of the line is $\frac{-3}{5}$ and the line passing through (4,-1).

Rewrite the above equation in slope intercept form.

$y=\frac{-3}{5}x+\frac{12}{5}-1$

$y=\frac{-3}{5}x+\frac{12-5}{5}$

$y=\frac{-3}{5}x+\frac{7}{5}$

The point slope form of a line is

$y=mx+b$

Where m is the slope and b is y-intercept.

Therefore the slope of the line is $\frac{-3}{5}$ and the y-intercept of the line is $\frac{7}{5}$ .

Slope is defined as

$m=\frac{Rise}{Run}$

Since the slope is negative, therefore the run of the line is considered on the left side. The line rise by 3 and run by 5, therefore we will add 7 in y and subtract 5 from x.

The y-intercept is $(0,\frac{7}{5})$ .

$(0-5,\frac{7}{5}+3)=(-5,\frac{22}{5})=(-5,4.4)$

Therefore we have three points (4,-1), (-5,4.4) and (0,1.4). Plot the point on the coordinate plane and connect them be a straight line.

7 0

2 years ago

Kojo wants to be an author. To improve his writing skills, every day after school he writes 3 pages of a story he is

koban [17]

If the number of days is d and he writes 3 pages for every d, then we can say

3d = 81

3 0

3 years ago