How to solve this math problem about convolution?

1. 📝 Identify: f(t) = e^(4t), g(t) = e^(2t) 2. 🧮 Convolution Formula: (f * g)(t) = ∫₀ᵗ f(τ)·g(t-τ) dτ = ∫₀ᵗ e^(4τ)·e^(2(t-τ)) dτ

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Home›Math›Solve: Compute the convolution: e^(4t) * e^(2t)

📐 MathLevel 2 — 🟢 Basicconvolution👁 18 views⏱ 1 min read

Solve: Compute the convolution: e^(4t) * e^(2t)

📝 Problem

Compute the convolution: e^(4t) * e^(2t)

1. 📝 Identify: ,

2. 🧮 Convolution Formula: (f * g)(t) = ∫₀ᵗ f(τ)·g(t-τ) dτ = ∫₀ᵗ e^(4τ)·e^(2(t-τ)) dτ

3. 📐 Evaluate integral: ∫₀ᵗ e^(4τ + 2τ) dτ = e^(2t) ∫₀ᵗ e^(2τ) dτ

= e^(2t) · [e^(2τ)/2]₀ᵗ

🔒 6 steps remaining

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1. 📝 Identify: ,

2. 🧮 Convolution Formula: (f * g)(t) = ∫₀ᵗ f(τ)·g(t-τ) dτ = ∫₀ᵗ e^(4τ)·e^(2(t-τ)) dτ

3. 📐 Evaluate integral: ∫₀ᵗ e^(4τ + 2τ) dτ = e^(2t) ∫₀ᵗ e^(2τ) dτ

= e^(2t) · [e^(2τ)/2]₀ᵗ

🔒 6 steps remaining

📐 Lv.2

Solve: Compute the convolution: e^(2t) * e^(5t)