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)
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
A. Find the indefinite integral.
B. Find the indefinite integral.
C. Find the derivative.
f(x) = x6 ·
log3(x)
Give your answer using the form below.
xA(B + C
logD(x))
A =
B =
C =
D =
D. Find the indefinite integral.
E. Find the area under the curve below from x = 1 to
x = 2. Give your answer correct to 3 decimal places.
F. Find the area under the curve below from x = 0 to...
Evaluate the integral: ∫−14 / x^2√x^2+100 dx
(A) Which trig substitution is correct for this integral?
x=−14sec(θ)
x=100sec(θ)
x=10tan(θ)
x=100sin(θ)
x=10sin(θ)
x=100tan(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?
1. (a) Evaluate the integral: ∫0 to 2 16 /x^2+4 dx
Your answer should be in the form kπkπ, where k is an integer. What
is the value of k?
Hint: d/dx arctan(x)=1/x^2+1
k=
(b) What is the upper bound for your error of your estimate if you
use the first 11 terms? (Use the alternating series estimation.)
=
2.
The function f(x)=8xln(1+x) is represented as a power
series
f(x)=∞∑n=0 cn x^n.
Find the specified coefficients in the power series....
) Find the following integral by using cylindrical
coordinates
\int _0^4\int _{-\sqrt{16-y^2}}^{\sqrt{16-y^2}}\int
_{-\sqrt{16-x^2-y^2}}^0\left(xy^2+6\right)\:dxdydz