Evaluating an Improper Integral In Exercises 17-32, determine whether the improperintegral diverges or converges. Evaluate theintegral if it converges. ∫ 0 ∞ 1 e x + e − x d x
Evaluating an Improper Integral In Exercises 17-32, determine whether the improperintegral diverges or converges. Evaluate theintegral if it converges. ∫ 0 ∞ 1 e x + e − x d x
Solution Summary: The author analyzes whether the improper integral displaystyle 'int' diverges or converges.
Evaluating an Improper Integral In Exercises 17-32, determine whether the improperintegral diverges or converges. Evaluate theintegral if it converges.
∫
0
∞
1
e
x
+
e
−
x
d
x
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.
1
(in blue), consider the functions g (in green) and h (in red) graphed below which are
x³/2
continuous on (0, ∞). Assuming the graphs continues in the same way as a goes to infinity, answer the following questions.
Given the function f(x) =
=
Algebra
Suppose that the function p(x) approximates the function f(x) with a maximum error of ε over the interval [a, b]. Then what is the error for the approximation of the integral [a,b] p(x)dx for the integral [a,b] f (x)dx.
Evaluate the integrals in Exercises 67–74 in terms of
a. inverse hyperbolic functions.
b. natural logarithms.
(2V3
•1/3
dx
6 dx
67.
68.
V4 + x?
V1 + 9x²
•1/2
dx
dx
70.
69.
1 – x²
5/4 1
•3/13
2
dx
dx
71.
72.
xV1 – 16x²
xV4 + x²
1/5
cos x dx
dx
73.
74.
o V1 + sin²x
xV1 + (ln x)²
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