Evaluate each integral using trig substitutions
1.) Integral of (3x^5dx)/(sqrt(16-x^2)
2.) Integral of (sqrt(x^2-16)dx)/x
3.) Integral of (6dx)/(16+16x^2)
Use Simpson’s Rule with n = 4 to approximate the value of the
definite integral ∫4 0 e^(−x^2) dx. (upper is 4, lower is 0)
Compute the following integrals (you may need to use Integration
by Substitution):
(a) ∫ 1 −1 (2xe^x^2) dx (upper is 1, lower is -1)
(b) ∫ (((x^2) − 1)((x^3) − 3x)^4)dx
Evaluate the integral. (Use C for the constant of
integration.)
(x^2-1)/(sqrt(25+x^2)*dx
Evaluate the integral. (Use C for the constant of
integration.)
dx/sqrt(9x^2-16)^3
Evaluate the integral. (Use C for the constant of
integration.)
3/(x(x+2)(3x-1))*dx
1. Approximate the integral,
exp(x), from 0 to 1,
using the composite midpoint rule, composite trapezoid rule, and
composite Simpson’s method. Each method
should involve exactly n =( 2^k) + 1 integrand evaluations, k = 1 :
20. On the same plot, graph the absolute error
as a function of n.
4 a) Find the Fourier Integral representation of ?(?) = 1 ?? |?|
< 1
0 ?? |?| > 1
b) Find the Fourier Sine Transform of ?(?) = ? −|?| . Hence
evaluate ∫ ?????? 1+?2 ??.