A)14 xy + 3 xy + 2[x[y - 17) Simplify the expression.
1 answer:
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Answer:
⁵/₃ ln 2
Step-by-step explanation:
∫₀¹ ∫√ₓ¹ 5 / (y³ + 1) dy dx
We want to change the order of integration. To do this, we start by graphing the region contained by the four limits.
x = 0, x = 1
y = √x, y = 1
(Notice that y = √x is the same as x = y²).
Once we've graphed the region, we need to write the domain of x in terms of y. In this case, 0 < x < y².
Then, we find the range: 0 < y < 1.
Now we can rewrite the integral:
∫₀¹ ∫₀ʸ² 5 / (y³ + 1) dx dy
Notice that the integrand itself, 5 / (y³ + 1), does not change. Only the limits have changed.
Solve the integral.
∫₀¹ [ 5 / (y³ + 1) x |₀ʸ² ] dy
∫₀¹ [ 5y² / (y³ + 1) ] dy
⁵/₃ ∫₀¹ [ 3y² / (y³ + 1) ] dy
(⁵/₃ ln|y³ + 1|) |₀¹
⁵/₃ ln|1³ + 1| − ⁵/₃ ln|0³ + 1|
⁵/₃ ln 2
Answer:
Written in Python
def sums(n):
total = 0
for i in range(1,n+1):
if i%2 == 0:
total = total + i*2
else:
total = total + i
return(total)
Step-by-step explanation:
The function is written in Python
def sums(n):
This initializes total to 0
total = 0
This iterates through the integers that makes up n i.e. 1,2,3.....n
for i in range(1,n+1):
This checks if current digit is even
if i%2 == 0:
If yes, it adds the double of the digit
total = total + i*2
else:
If otherwise, it adds the digit
total = total + i
This prints the calculated sum or total
return(total)
To call the function from main, use the following:
print(sums(n))
Where n is a positive integer. i.e.