Integration by substitution is used when direct integration is not feasible. Method simplifies complex functions by reducing them to standard form. Integration becomes f(g(t)).g'(t).dt when x = g(t)
Integration of UV formula finds integrals of product of two functions. Formula exists in two forms: ∫uv dx = u∫v dx - ∫(u'∫v dx) dx. Also known as integration by parts or product rule
Integration by parts transforms antiderivatives into simpler integrals. Formula uses product rule to find integrals of function products. Brook Taylor discovered it in 1715
Simpson's Rule approximates integrals using quadratic polynomial approximations. Named after mathematician Thomas Simpson, it extends trapezoidal rule. Divides interval into smaller sections and fits parabolic curves
Integration by Parts is used when two functions are multiplied together. Formula: ∫u v dx = u∫v dx − ∫u'(∫v dx) dx. Method involves choosing u, differentiating u, integrating v, and rearranging
Equations are y = 2x - x² = -x. Solutions are x = 0 and x = 3. Final equation becomes y = -x² + 2x