Math Notes

Integral Calculus

Integration techniques & applications—area, volume, accumulated change, work—with guided solutions.

Solved Problems

Area of Polar Curves

Find the area enclosed by r = 2a Cos<sup>2</sup> θFind the area enclosed by r = 2a Cos θ

Integration

Evaluate the integral of \( \sec \theta \).Integrate dx / (x-2)(x+1)What is the integral of ln x?Integrate x^3dx/(x^2-9)Integrate v^2 dv/(v+1)(v+2)(v+3)Integrate \( 7x^3 +4 x^2 dx\)

Area in a Bounded Region

What is the area bounded by the curve \(y = \sin {x}\) and \(y = \cos {x}\) and the x-axis in the first quadrant.Find the area bounded by \(y^2=4x\) and \(y+2x=12\)

Tags:

integral calculus integration area under curve volume by solids of revolution substitution integration by parts definite integral