0.96/6.25 points details my notes this question has several parts that must be completed sequentially. if…

0.96/6.25 points details my notes this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skippe tutorial exercise evaluate the integral. ∫e^7θ sin(8θ) dθ step 1 we will begin by letting u = sin(8θ) and dv = e^7θ dθ. then du = 8 cos(8θ) dθ and v = 1/7 e^7θ. step 2 after integration by parts we have ∫e^7θ sin(8θ) dθ = sin(8θ) 1/7 e^7θ - ∫e^7θ cos(8θ) dθ.

0.96/6.25 points details my notes this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skippe tutorial exercise evaluate the integral. ∫e^7θ sin(8θ) dθ step 1 we will begin by letting u = sin(8θ) and dv = e^7θ dθ. then du = 8 cos(8θ) dθ and v = 1/7 e^7θ. step 2 after integration by parts we have ∫e^7θ sin(8θ) dθ = sin(8θ) 1/7 e^7θ - ∫e^7θ cos(8θ) dθ.

Answer

Explanation:

Step1: Recall integration - by - parts formula

The integration - by - parts formula is $\int u\mathrm{d}v=uv-\int v\mathrm{d}u$. We have $u = \sin(8\theta)$, $\mathrm{d}v=e^{7\theta}\mathrm{d}\theta$, $\mathrm{d}u = 8\cos(8\theta)\mathrm{d}\theta$ and $v=\frac{1}{7}e^{7\theta}$.

Step2: Apply integration - by - parts

Substitute $u$, $v$, $\mathrm{d}u$ and $\mathrm{d}v$ into the integration - by - parts formula: $\int e^{7\theta}\sin(8\theta)\mathrm{d}\theta=\sin(8\theta)\frac{1}{7}e^{7\theta}-\int\frac{1}{7}e^{7\theta}\cdot8\cos(8\theta)\mathrm{d}\theta=\frac{1}{7}e^{7\theta}\sin(8\theta)-\frac{8}{7}\int e^{7\theta}\cos(8\theta)\mathrm{d}\theta$

Answer:

$\frac{1}{7}e^{7\theta}\sin(8\theta)-\frac{8}{7}\int e^{7\theta}\cos(8\theta)\mathrm{d}\theta$