Draw the region and evaluate the following integral(a) ∫10∫21(y+2x)dydx∫01∫12(y+2x)dydx (b) ∫10∫xx2xydydx∫01∫x2xxydydx (c) ∫π0∫πysinxxdxdy∫0π∫yπsinxxdxdy
Which one of the improper integrals below converges or
diverges?
[int _a ^b] means integral from a to b, we use
inf to indicate infinity.
a) [int _0 ^1] 1/x dx
b) [int _0 ^1] 1/x^(1/2) dx
c) [int _0 ^1] 1/x^2 dx
d) [int _1 ^inf] 1/x dx
e) [int _1 ^inf] 1/x^(1/2) dx
f) [int _1 ^inf] 1/x^2 dx
g) [int _1 ^inf] lnx / x^2 dx
h) [int _1 ^inf] lnx / x dx
i) [int _(-inf)...
Evaluate the double integral explicitly by reversing the order
of integration:? Integral from 0 to 8 and integral from (sub3
square root of y) to 2 ex dxdy
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
Evaluate the integral Integral from 1 divided by 2 to 1 left
parenthesis x Superscript negative 3 Baseline minus 15 right
parenthesis dx using the Fundamental Theorem of Calculus.