Question

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

3x+C
5x+6
x+C
4x+C

Answer 1

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Answer on Question #46045– Math – Integral Calculus

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

$$3x + C$$ $$5x + 6$$ $$x + C$$ $$4x + C$$

Solution.

At first, we will find the indefinite integral:

$$I = \int 5dx = 5 \int dx = 5x + C.$$

We have condition that $I = 16$, when $x = 2$. Hence, we can define constant $C$:

$$16 = 5 \cdot 2 + C, \text{ hence } C = 16 - 10 = 6.$$

**Answer**: the second answer is correct

$$I = 5x + 6.$$