Answer:
a. Trapezoidal Rule- 9.413607
b. Midpoint Rule-9.393861
c. Simpson's Rule -9.400407
Step-by-step explanation:
a. We use n=8 for this integral, .
Therefore the integral range is
#For the Trapezoidal Rule:
Hence, the approximate integral value using Trapezoidal rule is 9.413607
b.For the Midpoint Rule, we calculate the integral as:
is the midpoint of the interval.
From our interval , the applicable intervals are
We therefore have the integral value as:
Hence, the approximate integral value using the Midpoint Rule is 9.393861
c. For the Simpson's Rule, we calculate the integral rule as follows:
We then have:
Hence, the approximate integral value using the Simpson's Rule is 9.400407