Question

homework 1: 1.1-1.4 review
score: 15/17 answered: 12/13
question 13
use the fundamental theorem of calculus to find the area between the horizontal axis, the graph of ( f(x) = 6x + 5 ), and the lines ( x = 4 ) and ( x = 7 ).
the area is square units.
question help: video

Explanation:

Step1: Find antiderivative of $f(x)$

The antiderivative of $f(x)=6x+5$ is $F(x)=3x^2+5x + C$ (the constant $C$ cancels out in definite integration, so we can ignore it).

Step2: Apply Fundamental Theorem of Calculus

We calculate $F(7)-F(4)$:
First, compute $F(7)$:
$F(7)=3(7)^2+5(7)=3(49)+35=147+35=182$
Then compute $F(4)$:
$F(4)=3(4)^2+5(4)=3(16)+20=48+20=68$
Subtract: $F(7)-F(4)=182-68$

Answer:

114 square units