Recent content by sugarxsweet

Help, please?

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 =...

Thanks!

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!

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...

Sorry, stupid question - if there's both u and v, how do I choose which one goes with which?

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?