Evaluate the following integral.
$\int_{\ln (3 π / 2)}^{\ln (11 π / 6)} 10 e^{v} \cos e^{v} d v$

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Answer

The final answer is $5 \sqrt{3} + \frac{35 π}{6}$

Steps

Step 1 ：Given the integral $\int_{\ln (3 π / 2)}^{\ln (11 π / 6)} 10 e^{v} \cos e^{v} d v$

Step 2 ：We can use the method of substitution. Let $u = e^{v}$ , then $d u = e^{v} d v = u d v$ . So the integral becomes $\int 10 u \cos (u) d u$ from $u = 3 π / 2$ to $11 π / 6$

Step 3 ：We can solve this integral by using the method of integration by parts, where we let $u = u$ and $d v = 10 \cos (u) d u$ . Then $d u = d u$ and $v = 10 \sin (u)$

Step 4 ：The formula for integration by parts is $\int u d v = u v - \int v d u$

Step 5 ：After calculating the integral, we substitute the limits of integration back in to get the final answer

Step 6 ：The final answer is $5 \sqrt{3} + \frac{35 π}{6}$

Evaluate the following integral.∫ln⁡(3π/2)ln⁡(11π/6)10evcos⁡evdv

Answer

Popular Problems

Evaluate the following integral.
$\int_{\ln (3 π / 2)}^{\ln (11 π / 6)} 10 e^{v} \cos e^{v} d v$