Calculus Mastery Suite
Integral Solver
Reverse the process of differentiation instantly. Find antiderivatives and master the fundamental theorem of calculus.
Integration Solver
Power Rule for Integration: ∫ axⁿ dx
∫
x
dx
Result (Antiderivative)1x^4 + C
The Constant C
Don't forget the constant of integration (+ C). When we integrate, we find a family of functions, and 'C' represents any constant that would differentiate to zero.
What is Integration?
Integration is the reverse process of differentiation. While differentiation finds the slope of a curve, integration finds the area under the curve.
The Golden Rule
∫ xⁿ dx = (xⁿ⁺¹) / (n+1) + C
Note: Valid for n ≠ -1
Practical Uses
Area: Finding the total space under a graph.
Volume: Calculating the size of 3D objects via rotation.
Probability: Determining odds in continuous distributions.
Energy: Calculating total work done by a force.
Integration is used in bridge design to calculate stress distribution across the entire structure.