Answer:
The integral symbol in the previous definition should look familiar. We have seen similar notation in the chapter on Applications of Derivatives, where we used the indefinite integral symbol (without the a and b above and below) to represent an antiderivative. Although the notation for indefinite integrals may look similar to the notation for a definite integral, they are not the same. A definite integral is a number. An indefinite integral is a family of functions. Later in this chapter we examine how these concepts are related. However, close attention should always be paid to notation so we know whether we’re working with a definite integral or an indefinite integral.
Integral notation goes back to the late seventeenth century and is one of the contributions of Gottfried Wilhelm Leibniz, who is often considered to be the codiscoverer of calculus, along with Isaac Newton. The integration symbol ∫ is an elongated S, suggesting sigma or summation. On a definite integral, above and below the summation symbol are the boundaries of the interval, \left[a,b\right]. The numbers a and b are x-values and are called the limits of integration; specifically, a is the lower limit and b is the upper limit. To clarify, we are using the word limit in two different ways in the context of the definite integral. First, we talk about the limit of a sum as n\to \infty . Second, the boundaries of the region are called the limits of integration.
We call the function f(x) the integrand, and the dx indicates that f(x) is a function with respect to x, called the variable of integration. Note that, like the index in a sum, the variable of integration is a dummy variable, and has no impact on the computation of the integral.
his leads to the following theorem, which we state without proof.
Step-by-step explanation:
Answer:
(Thermometer B reading - Thermometer A reading)
Step-by-step explanation:
The thermometer reading aren't given in the question.
However, hypothetically.
The difference between two temperature values (morning and evening values) would be :
Temperature in the evening - morning temperature
Therefore,
If ;
Thermometer A reading = morning temperature
Thermometer B reading = evening temperature
Difference in the temperature :
(Thermometer B reading - Thermometer A reading)
Answer:
The watermelon weighs more.
Step-by-step explanation:
I know this because 1 kilogram is equal to 2.20462 pounds. This means that 7.5 kilograms weighs as much as 16.5347 pounds. 16.5347 is greater than 12, so this means the watermelon weighs more.
Square root 156.25 to get the values of the sides of the square. You will get 12.5m for each side.
Now that you have the side values, use Pythagoras' Theorem to solve for the diagonal. Let's call the diagonal x,
c^2 = a^2 + b^2
x^2 = 12.5^2 + 12.5^2
= 312.5
Square root both sides to get x,
x = 17.68m (2 d.p)
HOPE THIS HELPED! Ask me if there is anything you don't understand from this working :D
