I have the equation:1τ∫0τAsin⁡(Ωt)⋅Asin⁡(Ω(t−λ))dtfor which the attempted solution is to convert the sine terms into complex natural exponents (engineering notation using j as imaginary unit) asA2τ∫0τejΩt−e−jΩt2j⋅ejΩ(t−λ)−e−jΩ(t−λ)2jdtthe next step in the solution moves the 12j term outside of the integral to form−A24τ∫0τ(ejΩt−e−jΩt)⋅(ejΩ(t−λ)−e−jΩ(t−λ))dtI'm struggling to understand how 12j→−14 when being moved out of the integral.

Question

I have the equation:1τ∫0τAsin⁡(Ωt)⋅Asin⁡(Ω(t−λ))dtfor which the attempted solution is to convert the sine terms into complex natural exponents (engineering notation using j as imaginary unit) asA2τ∫0τejΩt−e−jΩt2j⋅ejΩ(t−λ)−e−jΩ(t−λ)2jdtthe next step in the solution moves the 12j term outside of the integral to form−A24τ∫0τ(ejΩt−e−jΩt)⋅(ejΩ(t−λ)−e−jΩ(t−λ))dtI&#039;m struggling to understand how 12j→−14 when being moved out of the integral.

memantangti17 · Accepted Answer

You&#039;re moving out  12j⋅12j=−14 , not just 12j

I have the equation: \(\displaystyle{\frac{{{1}}}{{\tau}}}{\int_{{{0}}}^{{\tau}}}{A}{\sin{{\left(\Omega{t}\right)}}}\cdot{A}{\sin{{\left(\Omega{\left({t}-\lambda\right)}\right)}}}{\left.{d}{t}\right.}\) for which the attempted

Answered question

Answer & Explanation

New Questions in Integral Calculus