Equations are y = 2x - x² = -x. Solutions are x = 0 and x = 3. Final equation becomes y = -x² + 2x
Area under a curve is calculated using the formula A = ∫a,b f(x) dx. The integral must be definite with known limits. The power rule is used to set up the integration. The fundamental theorem relates the integral to the difference between the limits
Online tool for evaluating definite integrals with step-by-step solutions. Requires input of function and integration bounds. Displays result as numerical value or indicates divergence
The derivative of an indefinite integral equals the original function. For any function f(x), d/dx ∫ f(x) dx = f(x)
The integral of arctan is ∫tan-1x dx = x tan-1x - ½ ln |1+x²| + C. Integration is the process of reverse differentiation. The constant C is the constant of integration
Integration of x^2 equals x³/³ + C, where C is the integration constant. Integration is the reverse process of differentiation. Integration gives the area under the curve of f(x) = x²