Question

evaluate the integral.
int_{1}^{2}(2 x+7) d x
int_{1}^{2}(2 x+7) d x=square

Explanation:

Step1: Apply integral sum rule

$$\int_{1}^{2}(2x + 7)dx=\int_{1}^{2}2xdx+\int_{1}^{2}7dx$$

Step2: Evaluate $\int_{1}^{2}2xdx$

Use power rule $\int x^n dx=\frac{x^{n + 1}}{n+1}+C(n
eq - 1)$. For $y = 2x$, $\int_{1}^{2}2xdx=2\times\frac{x^{2}}{2}\big|_{1}^{2}=x^{2}\big|_{1}^{2}=2^{2}-1^{2}=4 - 1=3$

Step3: Evaluate $\int_{1}^{2}7dx$

Use $\int kdx=kx + C$ ($k$ is a constant). $\int_{1}^{2}7dx=7x\big|_{1}^{2}=7\times(2 - 1)=7$

Step4: Sum the results

$\int_{1}^{2}(2x + 7)dx=3 + 7=10$

Answer:

$10$