
Setting

, you have

. Then the integral becomes




Now,

in general. But since we want our substitution

to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means

, which implies that

, or equivalently that

. Over this domain,

, so

.
Long story short, this allows us to go from

to


Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

Then integrate term-by-term to get


Now undo the substitution to get the antiderivative back in terms of

.

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to
Answer: True
Step-by-step explanation:
The statement that a mixed number has a whole number part and a fractional part is true.
The mixed number is made up of a whole number, and a proper fraction. A mixed number simply means a number that is between any two whole numbers. Examples of mixed numbers are 4¾, 7½ etc.
A. Geometric
b. a curve sloping steeply upwards (exponential)
c. nth term an = a1r^(n-1)
nth term = 4(4)^(n-1)
Let's set up an equation.
smaller number = x
larger number = 2x - 5
Now set up the equation so that the larger number plus the smaller number adds up to 43.
x + 2x - 5 = 43
3x - 5 = 43 ( I added the x and 2x)
3x = 48 ( I added 5 to both sides)
x = 16 (I divided both sides by 3)
Now let's check it. Substitute 16 for every time there is an x.
16 + 2(16) - 5 = 43
16 + 32 - 5 = 43
48 - 5 = 43
43 = 43
It checks. x is equal to 16, so that means:
smaller number = 16
larger number = 27
Hope this helps =)
The father is 48 and the son is 20