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 TOPICS This page:   calculus    Search   Dr. Math See also the Internet Library:   calculus HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry 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 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 (1-sinX). 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 Quadruple-Angle 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 double-angle 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 anti-derivative 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 u-substitution. 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. Integration Problem [2/22/1995] How do you integrate the function: (tan 2x)^3 dx, in terms of x? Integration Questions [03/09/2001] Calculate the area of the finite region bounded by the curves y=x^2 and y=sqrt(x)... Page: []

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