Use a calculator or computer to make a table of values of left and right Riemann sums L n and R n for the integral ∫ 0 2 e − x 2 d x with n = 5, 10, 50, and 100. Between what two numbers must the value of the integral lie? Can you make a similar statement for the integral ∫ − 1 2 e − x 2 d x ? Explain.
Use a calculator or computer to make a table of values of left and right Riemann sums L n and R n for the integral ∫ 0 2 e − x 2 d x with n = 5, 10, 50, and 100. Between what two numbers must the value of the integral lie? Can you make a similar statement for the integral ∫ − 1 2 e − x 2 d x ? Explain.
Solution Summary: The author calculates the value of the integral displaystyle 'int', which lies between the two numbers, using the calculator.
Use a calculator or computer to make a table of values of left and right Riemann sums Ln and Rn for the integral
∫
0
2
e
−
x
2
d
x
with n = 5, 10, 50, and 100. Between what two numbers must the value of the integral lie? Can you make a similar statement for the integral
∫
−
1
2
e
−
x
2
d
x
? Explain.
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.
Use Euler's method to numerically integrate
dy
dx
-2x+12x² - 20x +8.5
from x=0 to x=4 with a step size of 0.5. The initial condition at x=0 is y=1. Recall
that the exact solution is given by y = -0.5x+4x³- 10x² + 8.5x+1
Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).
Find the point on the graph of the given function at which the slope of the tangent line is the given slope.
2
f(x)=8x²+4x-7; slope of the tangent line = -3
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY