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3 years ago

Evaluate this integral. I'm not sure how to evaluate integrals with absolute values.

Mathematics

1 answer:

SOVA2 [1]3 years ago

6 0

Answer:

Step-by-step explanation:

The first step is to understand what the integrand looks like. (See the graph below.)

It is -1 for x < 0 and +1 for x > 0. Thus, the value of this integral is ...

$\int\limits^0_{-1} {-1} \, dx + \int\limits^2_0 {1} \, dx=-1+2=1$

_____

Essentially, you treat the absolute value as a piecewise linear function. This is the same way you treat an absolute value in any equation or inequality.

Here, this means you divide the integral into two parts: one where the integrand is -x/x, and one where it is +x/x.

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Stardust the unicorn, covered a distance of 50 miles on his first trip to the forest. On a later trip he travelled 300 miles whi

jok3333 [9.3K]

His new time compared with the old time was increased by factor of 2

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

<em>a = acceleration (m / s²)v = final velocity (m / s)</em>

<em>u = initial velocity (m / s)</em>

<em>t = time taken (s)</em>

<em>d = distance (m)</em>

Let us now tackle the problem!

This problem is about Kinematics.

In this problem we assume that the unicorn is moving at a constant speed so that the acceleration is zero.

<u>Given:</u>

first distance = d₁ = 50 miles

second distance = d₂ = 300 miles

v₂ = 3 v₁

<u>Unknown:</u>

t₂ : t₁ = ?

<u>Solution:</u>

To find his new time , we will use the following formula.

$v_2 = 3 v_1$

$\frac{d_2}{t_2} = 3 \times \frac{d_1}{t_1}$

$\frac{300}{t_2} = 3 \times \frac{50}{t_1}$

$\frac{300}{t_2} = \frac{150}{t_1}$

$t_2 = \frac{300}{150} \times t_1$

$\large {\boxed {t_2 = 2 \times t_1} }$

<h3>Learn more</h3>

Velocity of Runner : brainly.com/question/3813437

Kinetic Energy : brainly.com/question/692781

Acceleration : brainly.com/question/2283922

The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Sperm , Whale , Travel

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3 years ago

The radius of the base of a right circular cone is 4 in., and its slant height is 15 in. If the radius and the slant height are

alukav5142 [94]

Answer:

Step-by-step explanation:

radius r = 4 in

slant height L = 15 in

base area = πr² = 16π in²

lateral area = πrL = 60π in²

surface area = 76π in²

r = 4×6, L = 15×6

base area = (4×6)²π = 16π×36

lateral area = 60π×36

surface area is multiplied by 36

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3 years ago

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Delvig [45]

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I hope this helps.

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3 years ago

Solve for b.<br> 7<br> 10b+ 18 = 28<br> Answer: 6<br> Submit Answer

azamat

Answer:

False B=1

Step-by-step explanation:

10b+18=28

Subtract 18 both sides.

10b=10

Divide 10 both sides.

b=1

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