Answer to Question #217126 in Calculus for Akhona Klanisi

Question

Question  2

Evaluate the definite integral         

$\intop$¹₀ 18e^3x+1dx (round to an integer).

 

1.      322

2.      311

3.      932

4.      965

Answer 1

To solve this integral, we have to consider that

$e^{3x+1}=e^u \\ u=3x+1, u(1)=4, u(0)=1 \\ \implies du=3dx$

With that information we proceed and find:

$I=∫^1_0 18e^{3x+1}dx=6(∫^1_0 3e^{3x+1}dx) \\ \implies I=6(∫^4_1 e^{u}du)=6 \left( \Big \lbrack e^{u}\Big \rbrack_1^4 \right)=6(e^4-e^1)$

$\implies I\approxeq 6(54.5981-2.7183)\approxeq311.2788\approxeq311$

In conclusion, $\intop$¹₀ 18e^3x+1dx (round to an integer) is equal to option 2. 311.

Reference:

• Varberg, D. E., Purcell, E. J., & Rigdon, S. E. (2007). Calculus with differential equations. Pearson/Prentice Hall.