convolution 相关的数学解题方法?

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

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📐 数学难度 2 — 🟢 Basicconvolution👁 18 浏览次数⏱ 1 min read

Solve: Compute the convolution: e^(1t) * e^(4t)

📝 Problem

Compute the convolution: e^(1t) * e^(4t)

1. 📝 Identify: ,

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

3. 📐 Evaluate integral: ∫₀ᵗ e^(1τ + 4τ) dτ = e^(4t) ∫₀ᵗ e^(-3τ) dτ

= e^(4t) · [e^(-3τ)/-3]₀ᵗ

🔒 6 步剩余

了解更多关于数学中convolution的知识。

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拍照或输入题目 — AI逐步解答

1. 📝 Identify: ,

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

3. 📐 Evaluate integral: ∫₀ᵗ e^(1τ + 4τ) dτ = e^(4t) ∫₀ᵗ e^(-3τ) dτ

= e^(4t) · [e^(-3τ)/-3]₀ᵗ

🔒 6 步剩余

📐 Lv.2

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