1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx)
(a) What is the first step of your ‘new’ integral?
(b) What is the final antiderivative step before evaluating?
(c) What is the answer in simplified exact form?
2) indefinite integral (cos^2 2theta) / (cos^2 theta) dtheta
(a) What is the first step of your ‘new’ integral?
(b) What is the simplified integral before taking the
antiderivative?
(c) What is the answer in simplified form?
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....