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.
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.
sec² 0
d0 converge or diverge.
3
2. Determine whether the improper integral |
1- tan 0
Hence evaluate the integral.
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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