evaluate the integral.
int_{4}^{3}(2 x + 4) d x
int_{4}^{3}(2 x + 4) d x = square (simplify your answer.)

Question

evaluate the integral.
 int_{4}^{3}(2 x + 4) d x
 int_{4}^{3}(2 x + 4) d x = square  (simplify your answer.)

Accepted Answer

# Explanation:
## Step1: Find antiderivative
The antiderivative of $2x$ is $x^{2}$ (using $\int x^{n}dx=\frac{x^{n + 1}}{n+1},n
eq - 1$ with $n = 1$) and the antiderivative of $4$ is $4x$. So the antiderivative of $2x + 4$ is $F(x)=x^{2}+4x$.
## Step2: Apply the fundamental theorem of calculus
$\int_{4}^{3}(2x + 4)dx=F(3)-F(4)$
$$
\begin{align*}
F(3)&=3^{2}+4\times3=9 + 12=21\
F(4)&=4^{2}+4\times4=16+16 = 32\
F(3)-F(4)&=21-32=- 11
\end{align*}
$$

# Answer:
$-11$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find antiderivative

Step2: Apply the fundamental theorem of calculus

Answer: