Homework Statement
Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method.
x^2 + (y-1)^2 = 1
Homework Equations
Cylindrical method: ∫2∏xf(x)dx
Slice Method: ∫A(x)dx
The Attempt at a Solution
x^2 + (y-1)^2 = 1
x =...
Sorry, I guess this is a question of trig then - how do I simplify my answer to the correct answer? It's probably something stupid but I'm having trouble figuring it out!
Homework Statement
Integrate cos(x)-cos(x-c) from 0 to c/2
Homework Equations
sin(x-c)=sinxcosc-cosxsinc
The Attempt at a Solution
sin(x)-sin(x-c) from 0 to c/2
=sin(c/2)-sin(c/2)cos(c)+cos(c/2)sin(c)-sin(0)+sin(-c)
=sin(c/2)-sin(c/2)cos(c)+cos(c/2)sin(c)-0-sin(c)
Correct...
Homework Statement
I am having issues figuring out the error involved in the trapezoidal and midpoint methods for ∫cos(x^2) from 0 to 1 with n=8
Homework Equations
|Et|<= k(b-a)^3/(12n^2)
|Em|<=k(b-a)^3/(24n^2)
The Attempt at a Solution
f(x)=cos(x^2)
f'(x)=-2xsin(x^2)...
Thanks! I got so far:
∫cos^n(x)dx from 0 to pi/2
=∫sin^n(pi/2-x)dx from 0 to pi/2
=∫sin^n(-x)dx from -pi/2 to 0
=∫sin^n(x)dx from 0 to pi/2
Does this look right to you? Thanks for the hint!
Sorry, to clarify, the hint says:
Use a trigonometric identity and substitution. Do not solve the definite integrals
Given this information, how would you recommend solving?
Homework Statement
Given that n is a positive integer, prove ∫sin^n(x)dx=∫cos^n(x)dx from 0 -> pi/2
Homework Equations
Perhaps sin^2(x)+cos^2(x)=1? Not sure.
The Attempt at a Solution
I honestly don't even know where to start. Should I set u=sin(x) or cos(x)? Doesn't seem to get...
Homework Statement
Evaluate the following indefinite integral:
∫(sin(ln16x))/xdx
Homework Equations
The Attempt at a Solution
let u = ln16x
therefore du=16/16x=1/x
∫sinudu
=-cosu
=-cos(ln16x)
Why is this showing as the wrong answer?