Question

Determine l = ∫ 2 cos⁡ x dx, given that l=7, when x=

cosx + sinx + c

2 sin x + 5

sin x + c

cosec x + c

Answer 1

Determine $l = \int 2\cos \frac{\pi}{2} \, dx$, given that $l = 7$, when $x = 90$

a) $\cos x + \sin x + c$

b) $2\sin x + 5$

c) $\sin x + c$

d) $\csc x + c$

**Solution**

$$I = \int 2 \cos x \, dx = 2 \int \cos x \, dx$$

But

$$\int \cos x \, dx = \sin x + c$$

So

$$I = 2 (\sin x + c)$$

Let's find "c"

$$I = 7 = 2 (\sin 90 + c) = 2 (1 + c) \rightarrow c = 2.5$$

and

$$I = 2 \sin x + 5$$

Answer: b) $2 \sin x + 5$.