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Browse High School Calculus
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Chain rule.
Maximizing the volume of a box.
Maximizing the volume of a cylinder.
Volume of a tank.
What is a derivative?
 Integral of N^1 [09/26/1997]

How do I find the integral of a number raised to the 1st power?
 Integral of sin(x)/x [8/29/1996]

Is there a symbolic (not a numerical method) solution to the definite
integral of sin(x)/x from 0 to some value?
 Integral of Triangular Surface [8/9/1996]

Is it possible to numerically integrate S { 1/3 (x^3 i + y^3 j + 0
k) . n} dS where n is the unit normal to the surface S, a triangle
in a plane?
 Integral of Trig Function, Exponent [8/6/1996]

What is the integral of f(x)=(tanx)^1/2?
 Integral Problems [9/14/1995]

A student asks questions about convergence and divergence in integrals.
 Integrals and Trig Functions [4/6/1996]

The integral from pi to zero of the square root of (1sinX).
 Integrals in Polar Coordinates [04/15/2003]

How can I evaluate an expression like (sin(theta)*(constant)) for
theta = 0...2*Pi?
 Integrals of the Cosecant, and of the Square Root of a Sum of Squares [03/05/2016]

A teen seeks general strategies for integrating a few trigonometric
expressions. Doctor Peterson obliges, providing the big picture as well
as troubleshooting a couple of her algebraic missteps — and revealing that her derivation is, in fact, equivalent to the answer in her textbook.
 Integrals versus Antiderivatives [02/24/2001]

What is the difference between an integral and an antiderivative?
 Integral tan(x)? [6/10/1996]

What is the antiderivative of the function tan(x)?
 Integral using Substitution [4/11/1996]

Evaluate: xdx / (x^2+1)^(1/2), given u^2 = x^2+1.
 Integrate Cos 2a [08/15/2001]

The answer given in the book for integrating cos 2a is sin 2a/2. Does
this follow a pattern?
 Integrating 1/(1+x^n) [11/14/2001]

Are there methods of integrating functions of the form 1/(1+x^n)? I have
solved 1/(1+x^4) and am wondering about solutions for higher powers of x.
 Integrating 1/(sinx)^6 dx [02/25/2002]

What is the integration of 1/(sinx)^6 dx?
 Integrating a Product of Cosines [05/04/2005]

Let n and m be natural numbers. My book says that the integral from
pi to pi of the function f(x) = cos(nx) * cos(mx) is pi if n = m and
0 else. I can't figure out how to prove this.
 Integrating a QuadrupleAngle Trigonometric Expression or Two [01/13/2011]

A network engineer seeks help integrating a trigonometric expression with a cosine
term in its denominator (or is it the cotangent?). Using doubleangle identities and a
substitution, Doctor Ali provides a boost.
 Integrating Exponentials [5/27/1995]

What is the integral of 5^x dx ?
 Integrating exp(x^2) [11/09/2005]

It seems like all the ways of finding integral exp(x^2) involve
making it a double integral and using polar coordinates. I was
wondering if there is any way to do it without making it a double
integral?
 Integrating with the Arc Length Formula [10/19/1998]

Can you help me integrate functions using the arclength formula, e.g.
x^(2/3)+y^(2/3)=1 and y=e^x?
 Integrating X^x, Closed Form [10/31/1996]

How do you express the equation y = xcosx in terms of y?
 Integration [5/23/1996]

Integrate the following function: x^2 * e^(2x^2)
 Integration [5/29/1996]

What does integral of (cos(x).x(cub).sinh(x)square).dx mean, and what's
the answer?
 Integration [01/08/1998]

What is the integrated area if the antiderivative is undefined?
 Integration [02/17/1999]

Integrate x*tan^2 x with respect to x.
 Integration [03/30/1999]

Integrate (2  x^2)^4x dx.
 Integration by Partial Fractions [11/14/1996]

How do you integrate f(x) = x^2/[(x^4) + 1]?
 Integration by Parts [2/15/1995]

I need the integral from 0 to 1 of X^4*exp(x/2). Can you help?
 Integration by Parts [12/8/1995]

How do you Integrate: x^n/e^x ?
 Integration by Parts [5/24/1996]

How do you integrate x^x?
 Integration by Parts [01/07/1997]

How do you solve Int [sin (ln x)] dx?
 Integration by Parts [05/27/1997]

What is the integral of sec^3(x)?
 Integration by Parts [04/08/1999]

How does one find the integral of [(sec x)^3 dx]?
 Integration by Parts [05/02/1999]

Find the general integral of x*ln(x)1.
 Integration by Parts [04/10/2008]

How can I integrate e^x(x+1)/(x+2)^2 ?
 Integration Hints [02/23/1999]

Can you help me integrate (cos[x])^4?
 Integration of Natural Logs [02/12/1998]

Why does the natural log of x equal the integral of 1/t dt from 1 to x?
Why is INT[(1/t)dt] from 1 to x the natural log of x, or why was it
defined this way?
 Integration of Sin(x^2) [11/10/1997]

I have been given the solution in the form of Frensel's Sin, but it
explains nothing about how it was integrated. I am not looking for an
equation, I am looking for a reason!
 Integration of Trigonometric Function by Substitution [03/18/1998]

Integrate [tan 2x dx] by usubstitution.
 Integration of Trigonometric Functions [05/28/1999]

How can I integrate sin(x)sin(2x).dx ?
 Integration Over a Complicated Region [11/1/1996]

Given a region defined by five relations simultaneously, find its area.
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