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Mathematics

( by Sónia Pais )

Integrals

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Hello friends, I left my notebook and maths textbook in my locker at school and I have a maths exam tomorrow. I'm desperate because I need to study... Can you help me solve these exercises so I can get 20 marks in the exam??

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Integrals

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Problems / Applications Indefinite Integral

Indefinite Integral

Problems / Applications Definite Integral

Definite Integral

Indefinite Integrals

Question 01

∫4x dx

is equal to:

01

Question 02

∫2 (4x-1)2 dx is equal to:

01

Question 03

Determine the particular solution, y=f(x), that satisfies the following conditions: f´(x)=6x2-6x e f(1)=-1

f(x)=2x3- 3x2

f(x)=12x- 6

f(x)=6x2- 6x-1

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Integrals

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Problems / Applications Indefinite Integral

Indefinite Integral

Problems / Applications Definite Integral

Definite Integral

Problems / Applications Indefinite Integral

Question 01

TourPeniche company has found that the rate of change of the average cost for one of its products is given by: , where x is the number of units and the cost is expressed in euros. The average cost to produce 20 units is 40 euros. From the options below, indicate which is the average cost function for the product?

02

Question 02

If the marginal cost of a certain product is given by: Cmg (x)=2x+100 with fixed costs of 200 euros, what is the expression for the Total Cost (CT) function?

02

Question 03

If the marginal cost of a certain product is given by MC(x) = 4x + 40 and the production of 25 units has a marginal cost of 3000 euros, what will be the cost to produce 30 units?

5300 euros

1250 euros

3750 euros

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Next Level

Integrals

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Problems / Applications Indefinite Integral

Indefinite Integral

Problems / Applications Definite Integral

Definite Integral

Definite Integral

Question 01

is equal to:

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Definite Integral

Question 01

is equal to:

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Definite Integral

Question 01

is equal to:

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Definite Integral

Question 01

is equal to:

03

Question 02

Knowing that and , calculate the value of :

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03

Question 02

Knowing that and , calculate the value of :

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03

Question 02

Knowing that and , calculate the value of :

03

Question 03

Knowing that and and calculate the value of :

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03

Question 03

Knowing that and and calculate the value of :

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03

Question 03

Knowing that and and calculate the value of :

Tenta outra vez

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03

Question 03

Knowing that and and calculate the value of :

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Next Level

Integrals

Complete all the activities and win a certificate!

Problems / Applications Indefinite Integral

Indefinite Integral

Problems / Applications Definite Integral

Definite Integral

Problems / Applications Definite Integral

Question 01

The area of the shaded region in the figure below is given by:

True

False

Problems / Applications Definite Integral

Question 01

The area of the shaded region in the figure below is given by:

The area of a region is given by: where f(x) is the upper bound of the function and h(x) is the lower bound of the function.

True

False

Question 02

04

It is known that, t months after the beginning of the year, the price of a certain product in supermarkets was given by: P(t) = 0.08t² - 0.18t + 1.6 (price per unit, in euros). Calculate the average price, per unit, of this product in the 2nd quarter of the year.

7,41

2,47

5,82

Question 03

04

A hotel kitchen assistant with t months' experience is able to peel potatoes a day. Calculate the average number of potatoes per day that a new helper will be able to peel during their first 3 months on the job. Round up the answer to the units.

541

824

720

360

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Integrals

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Integrals

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