Evaluate the definite integral of the algebraic function. $\int _ { 3 } ^ { 6 } ( 5 u + 4 ) d u$
Use a graphing utility to verify your results.
A)148.5
B)12
C)79.5
D)159
E)15

Question

Evaluate the definite integral of the algebraic function. $\int _ { 3 } ^ { 6 } ( 5 u + 4 ) d u$ 
Use a graphing utility to verify your results.
A)148.5
B)12
C)79.5
D)159
E)15

Quizplus · Accepted Answer

To evaluate the definite integral, we use the power rule of integration, which states that if f(x) = x^n, then the integral of f(x) dx is (x^(n+1))/(n+1) + C, where C is the constant of integration. 
Using this rule, we get:

∫(5u + 4) du = (5/2)*u^2 + 4u + C

Evaluating the definite integral from u=3 to u=6, we get:

((5/2)*6^2 + 4*6) - ((5/2)*3^2 + 4*3) = 79.5

Using a graphing utility, we can verify our result by plotting the function y = 5x + 4 and finding the area under the curve between x=3 and x=6, which is equal to the definite integral. The graph confirms that the area under the curve is approximately 79.5.

Evaluate the Definite Integral of the Algebraic Function ∫36(5u+4)du\int _ { 3 } ^ { 6 } ( 5 u + 4 ) d u∫36​(5u+4)du

Evaluate the Definite Integral of the Algebraic Function $\int _ { 3 } ^ { 6 } ( 5 u + 4 ) d u$