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Answer:
Yes, they are equivalent.
The graph of is a horizontal line. So the area under
on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.
The graph of is the upper half of a circle with radius
. It's symmetric about
, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is
.
Then use the fact that the definite integral is distributive over sums, meaning
Use PEMDAS to figure out the order of operations:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
Solve (-4 + -6) first, as this is in parentheses:
Solve 5.3 * -10 next, as this is multiplication:
Now we can solve the equation:
The answer is 63.
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
Solve (-4 + -6) first, as this is in parentheses:
Solve 5.3 * -10 next, as this is multiplication:
Now we can solve the equation:
The answer is 63.