convolution 相关的数学解题方法?

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

✦Đang tải AhaStep...

Solve: convolution e^(3t) * e^(5t) — Detailed Solution | AhaStep

Home›数学›Solve: convolution e^(3t) * e^(5t)

📐 数学难度 2 — 🟢 Basicconvolution👁 16 浏览次数⏱ 1 min read

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

📝 Problem

convolution e^(3t) * e^(5t)

1. 📝 Identify: ,

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

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

= e^(5t) · [e^(-2τ)/-2]₀ᵗ

🔒 6 步剩余

了解更多关于数学中convolution的知识。

🚀

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^(3τ)·e^(5(t-τ)) dτ

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

= e^(5t) · [e^(-2τ)/-2]₀ᵗ

🔒 6 步剩余

📐 Lv.2

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