♾
Improper Integrals Visualization
AP Calculus BC · Unit 6 Integration
Learning Objectives
Understand integrals over infinite intervals (a → ∞)
Understand integrals with infinite discontinuities
Rewrite as Limits: lim_{b→∞} ∫ₐᵇ f(x) dx
Determine Convergence vs Divergence
p-Test for Integrals
∫ [1 to ∞] 1/xᵖ dx
Converges if p > 1
Diverges if p ≤ 1
∫ [0 to 1] 1/xᵖ dx
Converges if p < 1
Diverges if p ≥ 1
Tags
improper integral
limits
convergence
infinity
INTEGRAL ∫ f(x) dx
∫₁^∞ 1/x² dx (Converges)
∫₁^∞ 1/x dx (Diverges)
∫₀^¹ 1/√x dx (Vertical Asymp)
∫_{−∞}^∞ e^(-x²) dx (Gaussian)
Limit Bound b
10.0
∫₁^b f(x) dx
—
Limit (b → ∞)
—