Question

Determine l = ∫ 5dx, given that l = 16, when x = 2.

a. x + c

b. sin2x + c

c. x + c

d. 5x + 6

Answer 1

Determine $l = \int 5 \, dx$, given that $l = 16$, when $x = 2$.

a. $x + c$

b. $\sin 2x + c$

c. $x + c$

d. $5x + 6$

**Solution**

$$l = \int 5 \, dx = 5 \int dx = 5(x + c) = 5x + 5c$$

We know that $l = 16$, when $x = 2$:

$$l = 16 = 5 * 2 + 5 * c = 10 + 5c \rightarrow c = \frac{6}{5}.$$

Let's put 'c' into equation for l:

$$l = 5x + 5 * \frac{6}{5} = 5x + 6.$$

Answer: d. $5x + 6$