Integrals Questions and Problems in Calculus

Free integral questions and problems in calculus are presented along with detailed solutions and applications.

Integrals and Their Applications

• Evaluate Integrals of Functions. Examples with detailed solutions.
• Integration by Parts. Tutorials with examples and detailed solutions and exercises with answers on how to use the technique of integration by parts to find integrals.
• Integration by Substitution. Tutorials with examples and detailed solutions and exercises with answers on how to use the powerful technique of integration by substitution to find integrals.
• Integral of ln x .
• Integral of Logarithmic Function to Any Base : Log_a (x) .
• Improper integrals with Infinite Intervals . Examples with detailed solutions.
• Trigonometric Substitution in Integrals . Examples with detailed solutions.
• Integral of Absolute Value of x .
• Integral of a^x .
• Evaluate Integrals Involving Quadratics Using Completing Square. Tutorials with examples and detailed solutions and exercises with answers on how to use the techniques completing square and substitution to evaluate integrals. .
• Integrals Involving sin(x) or cos(x) and Exponential. Tutorial to find integrals involving the product of sin(x) or cos(x) with exponential functions. Exercises with answers are at the bottom of the page.
• Integrals Involving sin(x) and cos(x) with odd power. Tutorial to find integrals involving the product of powers of sin(x) and cos(x) with one of the two having an odd power.
• Integrals Involving sin(x) with odd power.
• Integrals Involving sin(x) with even power.
• Find Area Under Curve. How to find the area under (and between) curves using definite integrals; tutorials, with examples and detailed solutions are presented.
• Find Area Between Curves. How to find the area between curves using definite integrals.
• Length of a Curve. Examples with detailed solutions.
• Calculate The Area in Polar Coordinates Curve. Examples with detailed solutions.
• Area of an Ellipse in Polar Coordinates .
• Find The Volume of a Solid of Revolution. How to find the volume of a solid of revolution generated by revolving a region bounded by the graph of a function around one of the axes using definite integrals?
• Volume by Cylindrical Shells Method. Find the volume of a solid of revolution generated by revolving a region bounded by the graph of a function around one of the axes using cylindrical shells.
• Partial Fractions Decompositions. How to decompose complicated algebraic fractions into simpler ones for integration?
• Integrals of Rational Functions using decomposition of Fractions.
• Online Partial Fractions Decomposition Calculator.
• Table of Integrals. A table of indefinite integrals of functions is presented below.
• Evaluate Integrals Involving Logarithms - Tutorial. Integrals with integrand containing logarithmic functions.
• Rules of Integrals with Examples including solutions and detailed explanations and exercises.
• Evaluate Integrals Involving Logarithms - tutorial. Tutorials, with examples and detailed solutions, exercises with answers, on integrals including logarithmic functions.
• Table of Laplace Transforms. A comprehensive table of Laplace transforms.
• Table of Fourier Transforms. A table of Fourier transforms.
• Multiple Integrals Calculations and Applications.

Integrals of Power of Trigonometric Functions

• Integral of sec(x)
• Integral of csc(x)
• Integral of sin^2(x)
• Integral of cos^2(x)
• Integral of sec^3(x)
• Integral of cos^3(x)
• Integral of sin^3(x)
• Integral of sec^4(x)
• Integral of tan^3(x)
• Integral of csc^3(x)
• Integral of sin^2(x)cos^2(x)
• Integral of sin^2(x)cos^3(x)
• Integral of sin^3(x)cos^2(x)
• Integral of sin^4(x)

Mathematical Formulas and Identities
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