Question

What is the area under the curve y=-x²+25 between x=0 and x=5?

Answer 1

The area under the curve y=-x²+25 between x=0 and x=5 is 83.33.

Step-by-step explanation:

The area under the curve y=-x²+25 between x=0 and x=5 can be found by integrating the function over this range. First, let's find the antiderivative of the function:

f(x) = -x² + 25

F(x) = (-1/3)x³ + 25x + C

Next, we evaluate the definite integral:

Area = F(5) - F(0) = [(-1/3)(5)³ + 25(5)] - [(-1/3)(0)³ + 25(0)]

Area = (125/3 + 125) - (0 + 0) = 250/3 = 83.33.