Estimating a definite integral Use a calculator and midpoint Riemann sums to approximate ∫ 1 25 2 x − 1 d x . Present your calculations in a table showing the approximations for n = 10 , 30. and 60 subintervals, assuming a regular partition. Make a conjecture about the exact value of the integral and verify your conjecture using the Fundamental Theorem of Calculus.
Estimating a definite integral Use a calculator and midpoint Riemann sums to approximate ∫ 1 25 2 x − 1 d x . Present your calculations in a table showing the approximations for n = 10 , 30. and 60 subintervals, assuming a regular partition. Make a conjecture about the exact value of the integral and verify your conjecture using the Fundamental Theorem of Calculus.
Solution Summary: The author explains how to approximate a definite integral by using calculator and midpoint Riemann sum. The exact value of the integral is 114.
Estimating a definite integral Use a calculator and midpoint Riemann sums to approximate
∫
1
25
2
x
−
1
d
x
. Present your calculations in a table showing the approximations for
n
=
10
, 30. and 60 subintervals, assuming a regular partition. Make a conjecture about the exact value of the integral and verify your conjecture using the Fundamental Theorem of Calculus.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
(a) Sketch the graph of the function on the given interval. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles. Calculate the midpoint Riemann sum for n=4, being sure to show all work. Use a calculator to calculate the left Riemann sum for n=64. f(x)= 1-x^2 on [0,2] ; n=4
(b) For the previous function on the given interval, calculate the definite integral using the infinite limit of the Right Riemann Sum.
WORK THROUGH ALL INTEGRALS
WORK THROUGH ALL LIMITS
TRIG INTEGRALS, LET THE EXPONENTS DETERMINE THE SUBSTITUTION
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