How to solve this math problem about convolution?

1. 📝 Identify: f(t) = e^(5t), g(t) = e^(3t) 2. 🧮 Convolution Formula: (f * g)(t) = ∫₀ᵗ f(τ)·g(t-τ) dτ = ∫₀ᵗ e^(5τ)·e^(3(t-τ)) dτ

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Home›Math›Solve: Compute the convolution: e^(5t) * e^(3t)

📐 MathLevel 2 — 🟢 Basicconvolution👁 20 views⏱ 1 min read

Solve: Compute the convolution: e^(5t) * e^(3t)

📝 Problem

Compute the convolution: e^(5t) * e^(3t)

1. 📝 Identify: ,

2. 🧮 Convolution Formula: (f * g)(t) = ∫₀ᵗ f(τ)·g(t-τ) dτ = ∫₀ᵗ e^(5τ)·e^(3(t-τ)) dτ

3. 📐 Evaluate integral: ∫₀ᵗ e^(5τ + 3τ) dτ = e^(3t) ∫₀ᵗ e^(2τ) dτ

= e^(3t) · [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^(5τ)·e^(3(t-τ)) dτ

3. 📐 Evaluate integral: ∫₀ᵗ e^(5τ + 3τ) dτ = e^(3t) ∫₀ᵗ e^(2τ) dτ

= e^(3t) · [e^(2τ)/2]₀ᵗ

🔒 6 steps remaining

📐 Lv.2

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